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Zvonimir Janko
Zvonimir Janko (26 July 1932 – 12 April 2022) was a Croatian mathematician who was the eponym of the Janko groups, sporadic simple groups in group theory. The first few sporadic simple groups were discovered by Émile Léonard Mathieu, which were then called the Mathieu groups. 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 J1. 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 b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bjelovar
Bjelovar ( hu, Belovár, german: Bellowar, Kajkavian: ''Belovar'') is a city in central Croatia. It is the administrative centre of Bjelovar-Bilogora County. At the 2021 census, there were 36,433 inhabitants, of whom 93.06% were Croats. History The oldest Neolithic location in this area is in Ždralovi, a suburb of Bjelovar, where, while building a basement for the house of Josip Horvatić, a dugout was found and identified as belonging to the Starčevo culture (5000 – 4300 BC). Finds from Ždralovi belong to a regional subtype of a late variant of the Neolithic culture. It is designated the Ždralovi ''facies'' of the Starčevo culture, or the final-stage Starčevo. There are also relics of the Korenovo culture, Sopot culture, Lasinja culture, and the Vučedol culture. as well as the Bronze and Iron Age cultures, found in the wider Bjelovar area. The more intensive development of the area began with the arrival of the Romans, who first came to the area between the Sava ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 in 1967 moved to the Mathematical Institute of the Hungarian Academy of Sciences in Budapest. His mathematical work was in algebraic number theory and abstract algebra, especially group theory. He proved that every finite tournament contains an odd number of Hamiltonian paths. He gave several proofs of the theorem on quadratic reciprocity. He proved important results concerning the invariants of the class groups of quadratic number fields. Iyanaga's pamphlet discusses and generalizes one of Rédei's theorems; it gives a "necessary and sufficient condition for the existence of an ideal class (in the restricted sense) of order 4 in a quadratic field ''k''() ..." In several cases, he determined if the ring of integers of the real quadratic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Janko Group J3
In the area of modern algebra known as group theory, the Janko group ''J3'' or the Higman-Janko-McKay group ''HJM'' is a sporadic simple group of order : 273551719 = 50232960. History and properties ''J3'' is one of the 26 Sporadic groups and was predicted by Zvonimir Janko in 1969 as one of two new simple groups having 21+4:A5 as a centralizer of an involution (the other is the Janko group ''J2''). ''J3'' was shown to exist by . In 1982 R. L. Griess showed that ''J3'' cannot be a subquotient of the monster group. Thus it is one of the 6 sporadic groups called the pariahs. J3 has an outer automorphism group of order 2 and a Schur multiplier of order 3, and its triple cover has a unitary 9-dimensional representation over the finite field with 4 elements. constructed it via an underlying geometry. It has a modular representation of dimension eighteen over the finite field with 9 elements. It has a complex projective representation of dimension eighte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marshall Hall (mathematician)
Marshall Hall Jr. (17 September 1910 – 4 July 1990) was an American mathematician who made significant contributions to group theory and combinatorics. Career Hall studied mathematics at Yale University, graduating in 1932. He studied for a year at Cambridge University under a Henry Fellowship working with G. H. Hardy. He returned to Yale to take his Ph.D. in 1936 under the supervision of Øystein Ore. He worked in Naval Intelligence during World War II, including six months in 1944 at Bletchley Park, the center of British wartime code breaking. In 1946 he took a position at Ohio State University. In 1959 he moved to the California Institute of Technology where, in 1973, he was named the first IBM Professor at Caltech, the first named chair in mathematics. After retiring from Caltech in 1981, he accepted a post at Emory University in 1985. Hall died in 1990 in London on his way to a conference to mark his 80th birthday. Contributions He wrote a number of papers of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Janko Group J2
In the area of modern algebra known as group theory, the Janko group ''J2'' or the Hall-Janko group ''HJ'' is a sporadic simple group of order : 2733527 = 604800 : ≈ 6. History and properties ''J2'' is one of the 26 Sporadic groups and is also called Hall–Janko–Wales group. In 1969 Zvonimir Janko predicted J2 as one of two new simple groups having 21+4:A5 as a centralizer of an involution (the other is the Janko group J3). It was constructed by as a rank 3 permutation group on 100 points. Both the Schur multiplier and the outer automorphism group have order 2. As a permutation group on 100 points J2 has involutions moving all 100 points and involutions moving just 80 points. The former involutions are products of 25 double transportions, an odd number, and hence lift to 4-elements in the double cover 2.A100. The double cover 2.J2 occurs as a subgroup of the Conway group Co0. J2 is the only one of the 4 Janko groups that is a subquotient of the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Janko Group J1
In the area of modern algebra known as group theory, the Janko group ''J1'' is a sporadic simple group of order : 233571119 = 175560 : ≈ 2. History ''J1'' is one of the 26 sporadic groups and was originally described by Zvonimir Janko in 1965. It is the only Janko group whose existence was proved by Janko himself and was the first sporadic group to be found since the discovery of the Mathieu groups in the 19th century. Its discovery launched the modern theory of sporadic groups. In 1986 Robert A. Wilson showed that ''J1'' cannot be a subgroup of the monster group. Thus it is one of the 6 sporadic groups called the pariahs. Properties The smallest faithful complex representation of ''J1'' has dimension 56.Jansen (2005), p.123 ''J1'' can be characterized abstractly as the unique simple group with abelian 2-Sylow subgroups and with an involution whose centralizer is isomorphic to the direct product of the group of order two and the alternating group A5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, Germany. Founded in 1386 on instruction of Pope Urban VI, Heidelberg is Germany's oldest university and one of the world's oldest surviving universities; it was the third university established in the Holy Roman Empire. Heidelberg is one of the most prestigious and highly ranked universities in Europe and the world. Heidelberg has been a coeducational institution since 1899. The university consists of twelve faculties and offers degree programmes at undergraduate, graduate and postdoctoral levels in some 100 disciplines. The language of instruction is usually German, while a considerable number of graduate degrees are offered in English as well as some in French. As of 2021, 57 Nobel Prize winners have been affiliated with the city o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 city limits, with a population of nearly 1 millionDemographia: World Urban Areas , Demographia.com, April 2016 on an area of . Located on the , the southeastern coast of France on the , at the foot of 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 renamed as the IMU Abacus Medal), the Carl Friedrich Gauss Prize, Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being List of International Congresses of Mathematicians Plenary and Invited Speakers, invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. It is one of the highest-ranked universities in the world. The institution moved to Newark, New Jersey, Newark in 1747, and then to the current site nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. It is a member of the Ivy League. The university is governed by the Trustees of Princeton University and has an endowment of $37.7 billion, the largest List of colleges and universities in the United States by endowment, endowment per student in the United States. Princeton provides undergraduate education, undergraduate and graduate education, graduate in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 city is located at the northern end of the Australian Capital Territory at the northern tip of the Australian Alps, the country's highest mountain range. As of June 2021, Canberra's estimated population was 453,558. The area chosen for the capital had been inhabited by Indigenous Australians for up to 21,000 years, with the principal group being the Ngunnawal people. European settlement commenced in the first half of the 19th century, as evidenced by surviving landmarks such as St John's Anglican Church and Blundells Cottage. On 1 January 1901, federation of the colonies of Australia was achieved. Following a long dispute over whether Sydney or Melbourne should be the national capital, a compromise was reached: the new capital would be buil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 metropolitan area known as Greater Melbourne, comprising an urban agglomeration of 31 local municipalities, although the name is also used specifically for the local municipality of City of Melbourne based around its central business area. The metropolis occupies much of the northern and eastern coastlines of Port Phillip Bay and spreads into the Mornington Peninsula, part of West Gippsland, as well as the hinterlands towards the Yarra Valley, the Dandenong and Macedon Ranges. It has a population over 5 million (19% of the population of Australia, as per 2021 census), mostly residing to the east side of the city centre, and its inhabitants are commonly referred to as "Melburnians". The area of Melbourne has been home to Aboriginal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
