Zvonimir Janko (26 July 1932 – 12 April 2022) was a Croatian mathematician who was the
eponym
An eponym is a person, a place, or a thing after whom or which someone or something is, or is believed to be, named. The adjectives which are derived from the word eponym include ''eponymous'' and ''eponymic''.
Usage of the word
The term ''epon ...
of the
Janko group
In the area of modern algebra known as group theory, the Janko groups are the four sporadic simple groups '' J1'', '' J2'', '' J3'' and '' J4'' introduced by Zvonimir Janko. Unlike the Mathieu groups, Conway groups, or Fischer groups, the Ja ...
s,
sporadic simple group
In mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups.
A simple group is a group ''G'' that does not have any normal subgroups except for the trivial group and ''G'' itself. The ...
s 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 ...
. The first few sporadic simple groups were discovered by
Émile Léonard Mathieu
Émile Léonard Mathieu (; 15 May 1835, in Metz – 19 October 1890, in Nancy) was a French mathematician. He is known for his work in group theory and mathematical physics. He has given his name to the Mathieu functions, Mathieu groups and Mathi ...
, which were then called the
Mathieu group
In group theory, a topic in abstract algebra, the Mathieu groups are the five sporadic simple groups ''M''11, ''M''12, ''M''22, ''M''23 and ''M''24 introduced by . They are multiply transitive permutation groups on 11, 12, 22, 23 or 24 objec ...
s. It was after 90 years of the discovery of the last Mathieu group that Zvonimir Janko constructed a new sporadic simple group in 1964. In his honour, this group is now called J
1. This discovery launched the modern theory of sporadic groups and it was an important milestone in the
classification of finite simple groups.
Biography
Janko was born in
Bjelovar, Croatia. He studied at the
University of Zagreb where he received Ph.D. in 1960, with advisor Vladimir Devidé. The title of the thesis was ''Dekompozicija nekih klasa nedegeneriranih Rédeiovih grupa na Schreierova proširenja'' (Decomposition of some classes of nondegenerate Rédei Groups on Schreier extensions), in which he solved a problem posed by
László Rédei
László Rédei (15 November 1900 – 21 November 1980) was a Hungarian mathematician.
Rédei graduated from the University of Budapest and initially worked as a schoolteacher. In 1940 he was appointed professor in the University of Szeged and i ...
.
He then taught physics at a high school in
Široki Brijeg
,
, nickname =
, motto =
, image_map = BiH municipality location Široki Brijeg.svg
, map_alt =
, map_caption = Location o ...
in
Bosnia and Herzegovina
Bosnia and Herzegovina ( sh, / , ), abbreviated BiH () or B&H, sometimes called Bosnia–Herzegovina and often known informally as Bosnia, is a country at the crossroads of south and southeast Europe, located in the Balkans. Bosnia and H ...
.
In 1962 Janko decided to leave
Yugoslavia
Yugoslavia (; sh-Latn-Cyrl, separator=" / ", Jugoslavija, Југославија ; sl, Jugoslavija ; mk, Југославија ;; rup, Iugoslavia; hu, Jugoszlávia; rue, label=Pannonian Rusyn, Югославия, translit=Juhoslavija ...
for Australia, where he first taught at
Monash University
Monash University () is a public research university based in Melbourne, Victoria, Australia. Named for prominent World War I general Sir John Monash, it was founded in 1958 and is the second oldest university in the state. The university has a ...
in
Melbourne
Melbourne ( ; Boonwurrung/Woiwurrung: ''Narrm'' or ''Naarm'') is the capital and most populous city of the Australian state of Victoria, and the second-most populous city in both Australia and Oceania. Its name generally refers to a met ...
. In 1964 he joined as full professor the
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 ...
in
Canberra
Canberra ( )
is the capital city of Australia. Founded following the federation of the colonies of Australia as the seat of government for the new nation, it is Australia's largest inland city and the eighth-largest city overall. The ci ...
. He then moved in 1968 to the United States, where he first was a visiting professor at
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
, and then full professor at the
Ohio State University
The Ohio State University, commonly called Ohio State or OSU, is a public land-grant research university in Columbus, Ohio. A member of the University System of Ohio, it has been ranked by major institutional rankings among the best publ ...
. In 1970 he was an invited speaker at the
International Congress of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the Nevanlinna Prize (to be rename ...
in
Nice
Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative c ...
. In 1972 Janko moved to Germany, where he was a full professor at
Heidelberg University
}
Heidelberg University, officially the Ruprecht Karl University of Heidelberg, (german: Ruprecht-Karls-Universität Heidelberg; la, Universitas Ruperto Carola Heidelbergensis) is a public research university in Heidelberg, Baden-Württemberg, ...
until his retirement in 2000.
Janko discovered his first sporadic simple group (called
J1) in 1964, when he was at the Australian National University. This was followed in 1966 by the prediction of
J2, whose existence was established in 1968 by
Marshall Hall and David Wales, and
J3, whose existence was established in 1969 by
Graham Higman and
John McKay. Finally, Janko found the group
J4 in 1975; its existence was confirmed in 1980 by
Simon P. Norton
Simon Phillips Norton (28 February 1952 – 14 February 2019) and others using computer calculations.
See also
*
Iwasawa group
__NOTOC__
In mathematics, a group is called an Iwasawa group, M-group or modular group if its lattice of subgroups is modular. Alternatively, a group ''G'' is called an Iwasawa group when every subgroup of ''G'' is permutable in ''G'' .
proved ...
*
Lyons group
In the area of modern algebra known as group theory, the Lyons group ''Ly'' or Lyons-Sims group ''LyS'' is a sporadic simple group of order
: 283756711313767
: = 51765179004000000
: ≈ 5.
History
''Ly'' is one of the 26 sporad ...
*
Thin group (finite group theory)
References
{{DEFAULTSORT:Janko, Zvonomir
1932 births
2022 deaths
People from Bjelovar
20th-century Croatian mathematicians
Yugoslav mathematicians
Group theorists
Faculty of Science, University of Zagreb alumni
Academic staff of the University of Zagreb
Ohio State University faculty
Academic staff of Heidelberg University
Academic staff of Monash University
Academic staff of the Australian National University