Cheryl Elisabeth Praeger (born 7 September 1948,
Toowoomba
Toowoomba ( , nicknamed 'The Garden City' and 'T-Bar') is a city in the Toowoomba Region of the Darling Downs, Queensland, Australia. It is west of Queensland's capital city Brisbane by road. The urban population of Toowoomba as of the 2021 C ...
,
Queensland
)
, nickname = Sunshine State
, image_map = Queensland in Australia.svg
, map_caption = Location of Queensland in Australia
, subdivision_type = Country
, subdivision_name = Australia
, established_title = Before federation
, established_ ...
) is an Australian mathematician. Praeger received BSc (1969) and
MSc degrees from the
University of Queensland
, mottoeng = By means of knowledge and hard work
, established =
, endowment = A$224.3 million
, budget = A$2.1 billion
, type = Public research university
, chancellor = Peter Varghese
, vice_chancellor = Deborah Terry
, city = B ...
(1974), and a doctorate from the
University of Oxford
, mottoeng = The Lord is my light
, established =
, endowment = £6.1 billion (including colleges) (2019)
, budget = £2.145 billion (2019–20)
, chancellor ...
in 1973 under direction of
Peter M. Neumann
Peter Michael Neumann OBE (28 December 1940 – 18 December 2020) was a British mathematician. His fields of interest included the history of mathematics and Galois theory.
Biography
Born in December 1940, Neumann was a son of the German-bo ...
. She has published widely and has advised 27 PhD students (as of March 2018). She is currently Emeritus Professor of Mathematics at the
University of Western Australia
The University of Western Australia (UWA) is a public research university in the Australian state of Western Australia. The university's main campus is in Perth, the state capital, with a secondary campus in Albany, Western Australia, Albany an ...
. She is best known for her works in
group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
,
algebraic graph theory
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph t ...
and
combinatorial design
Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of ''balance'' and/or ''symmetry''. These co ...
s.
Education
Praeger completed her high school education at
Brisbane Girls Grammar School
, motto_translation = Nothing without labour
, address = Gregory Terrace
, city = Spring Hill
, state = Queensland
, postcode = 4000
, country = Australia
, coordinates =
, type = Independent secondary d ...
. After graduating high school, Praeger went to the government vocational guidance section to inquire about how she could further study mathematics. The vocational guidance officer she spoke with tried to discourage her from studying mathematics further,
suggesting she become a teacher or a nurse because two other girls who came to him wanting to study maths were not able to pass their courses.
[ He reluctantly showed her an engineering course description, but she felt it did not have enough mathematics. So she left without getting much information that day, but did continue on to receive her bachelor's and master's degrees from the ]University of Queensland
, mottoeng = By means of knowledge and hard work
, established =
, endowment = A$224.3 million
, budget = A$2.1 billion
, type = Public research university
, chancellor = Peter Varghese
, vice_chancellor = Deborah Terry
, city = B ...
.
Having met several women on the mathematics staff during her undergraduate studies, the prospect of becoming a mathematician did not seem strange to her. During her first and second years she did honours studies in mathematics and physics, choosing to continue in mathematics after her second year.[ After completing her education at University of Queensland she was offered a research scholarship at ]Australian National University
The Australian National University (ANU) is a public research university located in Canberra, the capital of Australia. Its main campus in Acton encompasses seven teaching and research colleges, in addition to several national academies and ...
(ANU) but chose instead to take the Commonwealth Scholarship to the University of Oxford
, mottoeng = The Lord is my light
, established =
, endowment = £6.1 billion (including colleges) (2019)
, budget = £2.145 billion (2019–20)
, chancellor ...
and attended St Anne's College. At that point she knew she wanted to study algebra.
After earning her doctorate in 1973, she obtained a research fellowship at ANU. She had her first opportunity at teaching regular classes at the University of Virginia
The University of Virginia (UVA) is a Public university#United States, public research university in Charlottesville, Virginia. Founded in 1819 by Thomas Jefferson, the university is ranked among the top academic institutions in the United S ...
during the semester she worked there. Afterwards, she returned to ANU, where she met her future husband, John Henstridge, who was studying statistics. She was later offered a short-term position at the University of Western Australia
The University of Western Australia (UWA) is a public research university in the Australian state of Western Australia. The university's main campus is in Perth, the state capital, with a secondary campus in Albany, Western Australia, Albany an ...
, which turned into a long term position, where she currently works today.[ In 1989 she received the degree of Doctor of Science from the University of Western Australia for her work on permutation groups and algebraic graph theory.
]
Career
Her career has been largely spent in the Department of Mathematics and Statistics at the University of Western Australia. She was appointed full Professor in 1983 and was Head of the Department of Mathematics 1992–1994, inaugural Dean of Postgraduate Research Studies 1996–1998, Chair Promotions and Tenure Committee 2000–2004, Deputy Dean of the Faculty of Engineering Computing and Mathematics 2003–2006, ARC Professorial Fellow 2007. and ARC Federation Fellow in 2009.
Praeger has supervised over 30 graduate students and in 1997 she supervised the Honours research work of Akshay Venkatesh
Akshay Venkatesh (born 21 November 1981) is an Australian mathematician and a professor (since 15 August 2018) at the School of Mathematics at the Institute for Advanced Study. His research interests are in the fields of counting, equidistribu ...
who went on to win a 2018 Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...
, commonly regarded as the highest prize in mathematics.
During her career, Praeger has been invited to speak at many conferences, including ones in South Korea
South Korea, officially the Republic of Korea (ROK), is a country in East Asia, constituting the southern part of the Korea, Korean Peninsula and sharing a Korean Demilitarized Zone, land border with North Korea. Its western border is formed ...
, Singapore
Singapore (), officially the Republic of Singapore, is a sovereign island country and city-state in maritime Southeast Asia. It lies about one degree of latitude () north of the equator, off the southern tip of the Malay Peninsula, borde ...
, Hong Kong
Hong Kong ( (US) or (UK); , ), officially the Hong Kong Special Administrative Region of the People's Republic of China ( abbr. Hong Kong SAR or HKSAR), is a city and special administrative region of China on the eastern Pearl River Delt ...
, Morocco
Morocco (),, ) officially the Kingdom of Morocco, is the westernmost country in the Maghreb region of North Africa. It overlooks the Mediterranean Sea to the north and the Atlantic Ocean to the west, and has land borders with Algeria to ...
, Slovakia
Slovakia (; sk, Slovensko ), officially the Slovak Republic ( sk, Slovenská republika, links=no ), is a landlocked country in Central Europe. It is bordered by Poland to the north, Ukraine to the east, Hungary to the south, Austria to the s ...
, Slovenia
Slovenia ( ; sl, Slovenija ), officially the Republic of Slovenia (Slovene: , abbr.: ''RS''), is a country in Central Europe. It is bordered by Italy to the west, Austria to the north, Hungary to the northeast, Croatia to the southeast, an ...
, France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...
, Germany
Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...
, USSR
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nationa ...
, Belgium
Belgium, ; french: Belgique ; german: Belgien officially the Kingdom of Belgium, is a country in Northwestern Europe. The country is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeast, France to th ...
, Iran
Iran, officially the Islamic Republic of Iran, and also called Persia, is a country located in Western Asia. It is bordered by Iraq and Turkey to the west, by Azerbaijan and Armenia to the northwest, by the Caspian Sea and Turkmeni ...
, Italy
Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical re ...
, the Philippines
The Philippines (; fil, Pilipinas, links=no), officially the Republic of the Philippines ( fil, Republika ng Pilipinas, links=no),
* bik, Republika kan Filipinas
* ceb, Republika sa Pilipinas
* cbk, República de Filipinas
* hil, Republ ...
, and Japan
Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the north ...
.[
]
Awards, honours and memberships
Praeger is a Fellow of the Australian Academy of Science
The Australian Academy of Science was founded in 1954 by a group of distinguished Australians, including Australian Fellows of the Royal Society of London. The first president was Sir Mark Oliphant. The academy is modelled after the Royal Soci ...
, former president of the
Australian Mathematical Society
The Australian Mathematical Society (AustMS) was founded in 1956 and is the national society of the mathematics profession in Australia. One of the Society's listed purposes is to promote the cause of mathematics in the community by representing t ...
(1992–1994 and first female President of the Society). She was appointed as a Member of the Order of Australia
The Order of Australia is an honour that recognises Australian citizens and other persons for outstanding achievement and service. It was established on 14 February 1975 by Elizabeth II, Queen of Australia, on the advice of the Australian Gove ...
in 1999 and promoted to Companion in 2021.
Awards include:
* Honorary Doctor of Science from the Prince of Songkla University
Prince of Songkla University (PSU) ( th, มหาวิทยาลัยสงขลานครินทร์; ) is the first university in southern Thailand, established in 1967. The name of the university was granted by the King Bhumibol ...
, Thailand (1993).
* Fellow of the Australian Academy of Science
The Australian Academy of Science was founded in 1954 by a group of distinguished Australians, including Australian Fellows of the Royal Society of London. The first president was Sir Mark Oliphant. The academy is modelled after the Royal Soci ...
(1996).
* Member of the Order of Australia
The Order of Australia is an honour that recognises Australian citizens and other persons for outstanding achievement and service. It was established on 14 February 1975 by Elizabeth II, Queen of Australia, on the advice of the Australian Gove ...
for her service to mathematics in Australia, especially through research and professional associations (1999).
* Centenary Medal
The Centenary Medal is an award which was created by the Australian Government in 2001. It was established to commemorate the centenary of the Federation of Australia and to recognise "people who made a contribution to Australian society or go ...
of the Australian Government (2003).[
* Doctor Honoris Causis from the Université Libre de Bruxelles, Belgium (2005).
* Western Australian Scientist of the Year (2009).
* Moyal Medal of ]Macquarie University
Macquarie University ( ) is a public research university based in Sydney, Australia, in the suburb of Macquarie Park. Founded in 1964 by the New South Wales Government, it was the third university to be established in the metropolitan area of S ...
, Australia (2011; the first female recipient of the Medal since its establishment in 2000).
* 2011 Euler Medal of the Institute of Combinatorics and its Applications
The Institute of Combinatorics and its Applications (ICA) is an international scientific organization formed in 1990 to increase the visibility and influence of the combinatorial community. In pursuit of this goal, the ICA sponsors conferences, ...
(presented in 2017).
* Fellow of the American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
(2012).
* Thomas Ranken Lyle Medal
The Thomas Ranken Lyle Medal is awarded at most every two years by the Australian Academy of Science to a mathematician or physicist for his or her outstanding research accomplishments. of the Australian Academy of Science (2013; the first female recipient of the Medal since its establishment in 1935).
* George Szekeres Medal
The George Szekeres Medal is awarded by the Australian Mathematical Society for outstanding research contributions over a fifteen-year period. This award, established in 2001, was given biennially in even-numbered years until 2021 and has since bee ...
of the Australian Mathematical Society
The Australian Mathematical Society (AustMS) was founded in 1956 and is the national society of the mathematics profession in Australia. One of the Society's listed purposes is to promote the cause of mathematics in the community by representing t ...
(2014; the first female recipient of the Medal since its establishment in 2002).
* Honorary Member of the London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...
(2014).
* Honorary doctorate in Mathematics Education by Yazd University
Yazd University (YU, , ''Danushgah-e Yezd'') is a public research university in Yazd, Iran. It is a major state-funded research center in central Iran and the academic center of Yazd province and was the first comprehensive institute of higher e ...
, Iran (2015).
* Mehdi Behzad
Mehdi Behzad (Persian:مهدی بهزاد; born April 22, 1936) is an Iranian mathematician specializing in graph theory. He introduced his total coloring theory (also known as "Behzad's conjecture" or "the total chromatic number conjecture") dur ...
Prize of the Iranian Mathematical Society, for management in mathematics (2015).
* Honorary Doctor of Science from the University of Saint Andrews
(Aien aristeuein)
, motto_lang = grc
, mottoeng = Ever to ExcelorEver to be the Best
, established =
, type = Public research university
Ancient university
, endowment ...
, Scotland (2015).
* Inducted into both the Western Australian Women's Hall of Fame and the Western Australian Science Hall of Fame (2015).
* Honorary Doctor of Mathematics from the University of Queensland
, mottoeng = By means of knowledge and hard work
, established =
, endowment = A$224.3 million
, budget = A$2.1 billion
, type = Public research university
, chancellor = Peter Varghese
, vice_chancellor = Deborah Terry
, city = B ...
, Australia (2017).
* Honorary Doctor from the University of Primorska
University of Primorska (Slovenian ''Univerza na Primorskem'', Italian ''Università del Litorale'') is by age and size the third university in Slovenia. It is located in Koper, Izola, and Portorož and is named for the Slovenian Littoral region ...
, Slovenia (2018).
* Prime Minister's Prize for Science
The Prime Minister's Prizes for Science are annual Australian awards for outstanding achievements in scientific research, innovation, and teaching. The prizes have been awarded since 2000, when they replaced the Australia Prize for science.
Th ...
(2019).
* Kirk Distinguished Visiting Fellow at the Isaac Newton Institute
The Isaac Newton Institute for Mathematical Sciences is an international research institute for mathematics and its many applications at the University of Cambridge. It is named after one of the university's most illustrious figures, the mathema ...
in Cambridge (2020).
* Companion of the Order of Australia
The Order of Australia is an honour that recognises Australian citizens and other persons for outstanding achievement and service. It was established on 14 February 1975 by Elizabeth II, Queen of Australia, on the advice of the Australian Gove ...
for "eminent service to mathematics, and to tertiary education, as a leading academic and researcher, to international organisations, and as a champion of women in STEM careers". This is Australia's highest civic honour. (2021)
* Inaugural Ruby Payne-Scott
Ruby Violet Payne-Scott, BSc (Phys) MSc DipEd (Syd) (28 May 1912 – 25 May 1981) was an Australian pioneer in radiophysics and radio astronomy, and was one of two Antipodean women pioneers in radio astronomy and radio physics at the end of the ...
Medal and Lecture of the Australian Academy of Science (2021).
Since 2014, the Women in Mathematics Special Interest Group of the Australian Mathematical Society bestows the Cheryl E. Praeger Travel Awards
Cheryl is a female given name common in English speaking countries.
There are several prevailing theories about its etymology. The most common is that it has Italo-Celtic roots and is an Anglicised version of either the French name Cherie (from L ...
to female mathematicians. Since 2017 the Australian Mathematics Trust has awarded the Cheryl Praeger Medal to the best performing female contestants in the Australian Mathematics Competition The Australian Mathematics Competition is a mathematics competition run by the Australian Maths Trust for students from year 3 up to year 12 in Australia, and their equivalent grades in other countries. Since its inception in 1976 in the Australian ...
.
Praeger has also held memberships with the Combinatorial Mathematics Society of Australasia
The Combinatorial Mathematics Society of Australasia (CMSA) is a professional society of mathematicians working in the field of combinatorics. It is the primary combinatorics society for Australasia, consisting of Australia, New Zealand and neigh ...
, Institute of Combinatorics and its Applications
The Institute of Combinatorics and its Applications (ICA) is an international scientific organization formed in 1990 to increase the visibility and influence of the combinatorial community. In pursuit of this goal, the ICA sponsors conferences, ...
, Australian Mathematics Trust, American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
, and the London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...
. Her past affiliations have not been limited to academia.
Other activities
Praeger has been a member of the Curriculum Development Center of the Commonwealth Schools Commission, the Prime Ministers Science Advisory Council
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
, WISET Advisory Committee to the Federal Minister for Science on participation of women in Science, Engineering, and Technology, UWA Academy of Young Mathematicians Lectures, the Western Australian School Mathematics Enrichment Course Tutor, and Data Analysis Australia Pty Ltd. She has also served on the Australian Federation of University Women
Australian Graduate Women (AGW), founded in 1922, is the national organisation for Graduate Women in Australia. Previously known as the Australian Federation of University Women until 2009 and the Australian Federation of Graduate Women until Ap ...
(Western Australian Branch) and the Nedlands Primary School Council. Between 1992 and 2019 she was a board member of the Australian Mathematics Trust The Australian Mathematics Competition is a mathematics competition run by the Australian Maths Trust for students from year 3 up to year 12 in Australia, and their equivalent grades in other countries. Since its inception in 1976 in the Australian ...
. From 2001 to 2019 she chaired the Australian Mathematical Olympiad
Mathematics competitions or mathematical olympiads are competitive events where participants complete a mathematics, math test. These tests may require multiple choice or numeric answers, or a detailed written solution or proof.
International math ...
Committee. She is currently a member of the National Science and Technology Council.
Between 2007 and 2014 Praeger was a member of the executive committee of the International Mathematical Union
The International Mathematical Union (IMU) is an international non-governmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports ...
and between 2013 and 2016 a Vice President of the International Commission on Mathematical Instruction The International Commission on Mathematical Instruction (ICMI) is a commission of the International Mathematical Union and is an internationally acting organization focussing on mathematics education. ICMI was founded in 1908 at the International ...
.
Between 2014 and 2018 Praeger was Foreign Secretary of the Australian Academy of Science
The Australian Academy of Science was founded in 1954 by a group of distinguished Australians, including Australian Fellows of the Royal Society of London. The first president was Sir Mark Oliphant. The academy is modelled after the Royal Soci ...
. She was elected as a Member-at-Large of the executive board of the Association of Academies and Societies of Sciences in Asia (AASSA) for 2016–18 and accepted an invitation to Chair the AASSA Committee of Women in Science and Engineering (WISE). She is a Member of the executive committee of the Inter Academy Partnership - Science, 2017–19. Since 2019 she has been a member of the Committee for Freedom and Responsibility in Science of the International Science Council
The International Science Council (ISC) is an international non-governmental organization that unites scientific bodies at various levels across the social and natural sciences. The ISC was formed with its inaugural general assembly on 4 July 201 ...
.
Praeger promotes the involvement of women in mathematics by encouraging girls in primary and secondary schools with lectures, workshops, conferences and through the Family Maths Program Australia (FAMPA), which she was key in implementing in local primary schools. She is currently Patron of the Mathematical Association of Western Australia.
Personal life
In August 1975 Praeger married John Henstridge in Brisbane
Brisbane ( ) is the capital and most populous city of the states and territories of Australia, Australian state of Queensland, and the list of cities in Australia by population, third-most populous city in Australia and Oceania, with a populati ...
. They have two children, James (1979) and Tim (1982).
In addition to holding a doctorate in mathematics, she also holds an Associate in Music, Australia (AMusA) in piano performance and was a member of the University of Western Australia Collegium Musicum
The Collegium Musicum was one of several types of musical societies that arose in German and German-Swiss cities and towns during the Reformation and thrived into the mid-18th century.
Generally, while societies such as the (chorale) cultivated ...
between 1977 and 1985. She has been a member of the Uniting Church in Australia
The Uniting Church in Australia (UCA) was founded on 22 June 1977, when most congregations of the Methodist Church of Australasia, about two-thirds of the Presbyterian Church of Australia and almost all the churches of the Congregational Union ...
, Nedlands Parish since 1977, functioned as an elder from 1981 to 1987, and as an organist/pianist since 1985. She lists keyboard music among her stronger interests along with sailing, hiking, and cycling.
Research
Praeger published her first research paper in1970 while she was still an undergraduate. Since then she has become one of the most highly cited authors in pure mathematics, with (as of December 2022) over 450 publications total. She in known as a collaborator, with over 200 co-authors.
Praeger's research is centred around the mathematics of symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...
, including key work in group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
(especially group actions
In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism ...
and permutation groups
In mathematics, a permutation group is a group ''G'' whose elements are permutations of a given set ''M'' and whose group operation is the composition of permutations in ''G'' (which are thought of as bijective functions from the set ''M'' to ...
), combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...
, analysis of algorithms
In computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them. Usually, this involves determining a function that re ...
and complexity, discrete mathematics
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous f ...
and geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
. Major areas and results include:
* She has co-authored eleven papers with Peter Cameron, including the proof of Sims' Conjecture in 1983. This was an early application of the classification of finite simple groups
In mathematics, the classification of the finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or it belongs to a broad infinite class called the groups of Lie type, or else it ...
.
* With Jan Saxl
Jan Saxl (5 June 1948 – 2 May 2020) was a Czech-British mathematician, and a professor at the University of Cambridge. He was known for his work in finite group theory, particularly on consequences of the classification of finite simple groups ...
and Martin Liebeck
Martin Liebeck (born 23 September 1954) is a professor of Pure Mathematics at Imperial College London whose research interests include group theory and algebraic combinatorics.[permutation group
In mathematics, a permutation group is a group ''G'' whose elements are permutations of a given set ''M'' and whose group operation is the composition of permutations in ''G'' (which are thought of as bijective functions from the set ''M'' to it ...]
s, primitive permutation group
In mathematics, a permutation group ''G'' acting on a non-empty finite set ''X'' is called primitive if ''G'' acts transitively on ''X'' and the only partitions the ''G''-action preserves are the trivial partitions into either a single set or int ...
s, simple group
SIMPLE Group Limited is a conglomeration of separately run companies that each has its core area in International Consulting. The core business areas are Legal Services, Fiduciary Activities, Banking Intermediation and Corporate Service.
The d ...
s, and almost simple group In mathematics, a group is said to be almost simple if it contains a non- abelian simple group and is contained within the automorphism group of that simple group – that is, if it fits between a (non-abelian) simple group and its automorphism grou ...
s. Together they co-authored "On the O'Nan Scott Theorem for primitive permutation groups". It pertains to the classification of finite simple groups
In mathematics, the classification of the finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or it belongs to a broad infinite class called the groups of Lie type, or else it ...
, namely the classification of finite primitive permutation groups. The paper contains a complete self-contained proof of the theorem.
* Praeger later went on to generalise the O'Nan–Scott Theorem to quasiprimitive groups.[
An O'Nan-Scott Theorem for Finite Quasiprimitive Permutation Groups and an Application to 2-Arc Transitive Graphs, Journal of the London Mathematical Society, Volume s2-47, 1993, Pages 227–239]
* Praeger introduced normal quotients of graphs which allows the finite simple groups classification to be applied to analyse symmetric graphs and edge-transitive graph
In the mathematical field of graph theory, an edge-transitive graph is a graph such that, given any two edges and of , there is an automorphism of that maps to .
In other words, a graph is edge-transitive if its automorphism group acts t ...
s as well as Cayley graph
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayle ...
s. It is now a standard tool in algebraic graph theory
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph t ...
.
* With Peter M Neumann she developed and analysed the first randomised algorithm to recognise finite special linear group In mathematics, a matrix group is a group ''G'' consisting of invertible matrices over a specified field ''K'', with the operation of matrix multiplication. A linear group is a group that is isomorphic to a matrix group (that is, admitting a faithf ...
s. This led to the international matrix group recognition project and was extended to all finite classical groups by Praeger and Alice Niemeyer.
* She has co-authored several papers on symmetric graph
In the mathematical field of graph theory, a graph is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices and of , there is an automorphism
:f : V(G) \rightarrow V(G)
such that
:f(u_1) = u_2 and f(v_1) = v_2.
In oth ...
s and distance-transitive graph
In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices and at any distance , and any other two vertices and at the same distance, there is an automorphism of the graph that carrie ...
s with Tony Gardiner.
Selected publications
* with Martin Liebeck, Jan Saxl
''The maximal factorizations of the finite simple groups and their automorphism groups''
American Mathematical Society 1990
* with Leonard Soicher
''Low rank representations and graphs for sporadic groups''
Cambridge University Press 1997
* with Jason Fulman, Peter Neumann: ''A generating function approach to the enumeration of matrices in classical groups over finite fields'', American Mathematical Society 2005
* with Martin Liebeck, Jan Saxl
''Regular subgroups of primitive permutation groups''
American Mathematical Society 2010
* with Csaba Schneider
Groups and Cartesian Decompositions''
Cambridge University Press 2018
References
External links
Personal web page
Agnes Scott College
Agnes Scott College is a private women's liberal arts college in Decatur, Georgia. The college enrolls approximately 1,000 undergraduate and graduate students. The college is affiliated with the Presbyterian Church and is considered one of the ...
*
Summary of Cheryl Praeger's career
– by Bernhard Neumann
Bernhard Hermann Neumann (15 October 1909 – 21 October 2002) was a German-born British-Australian mathematician, who was a leader in the study of group theory.
Early life and education
After gaining a D.Phil. from Friedrich-Wilhelms Universit ...
in 1999.
Theorems by Cheryl Praeger at Theorem of the Day
* University of New South Wales
The University of New South Wales (UNSW), also known as UNSW Sydney, is a public research university based in Sydney, New South Wales, Australia. It is one of the founding members of Group of Eight, a coalition of Australian research-intensive ...
{{DEFAULTSORT:Praeger, Cheryl
1948 births
Living people
20th-century Australian mathematicians
21st-century Australian mathematicians
Australian women mathematicians
Group theorists
Combinatorialists
Members of the Order of Australia
Companions of the Order of Australia
Fellows of the Australian Academy of Science
Fellows of the American Mathematical Society
People from Toowoomba
University of Queensland alumni
Alumni of the University of Oxford
University of Western Australia faculty
20th-century women mathematicians
21st-century women mathematicians
20th-century Australian women