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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 (, , Czech language, Czech: ''Bělovar'' or ''Bělovár,'' Kajkavian dialect, Kajkavian: ''Belovar,'' Latin: ''Bellovarium'') is a city in central Croatia. In the Demographics of Croatia, 2021 census, its population was 36,316 . It is the administrative centre of Bjelovar-Bilogora County as well as one of the youngest cities in Croatia, officially founded in the year 1756. Name The origin of the modern name ''Bjelovar'' is a topic of debate; however, a prominent theory posits that the name is derived from the concept of "white land", a term historically used to describe land that was challenging to cultivate. Older records of names like Belublathya or Bjeloblaće i.e. "white mud", indicate this possibility. The name of the city itself consists of the Croatian adjective ', meaning ''white'', added to the Hungarian word ' or ''város'' which roughly translates to ''city'' or ''fortress''. Name history The name of a settlement similar to Bjelovar is mentioned severa ... [...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 fie ... [...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 : 50,232,960 = 273551719. 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 eigh ... [...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. Education and 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 numb ... [...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 : 604,800 = 2733527 : ≈ 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 mo ... [...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 (group theory), order : 175,560 = 233571119 : ≈ 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 Arnott Wilson, 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 pariah group, pariahs. Properties The smallest faithful complex representation of ''J1'' has dimension 56. ''J1'' can be characterized abstractly as the unique simple group with abelian Sylow theorems, 2-Sylow subgroups and with an Involution (mathematics), involution whose centralizer is isomorphic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heidelberg University
Heidelberg University, officially the Ruprecht Karl University of Heidelberg (; ), 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 after Prague (1347) and Vienna (1365). Since 1899, it has been a coeducational institution. Heidelberg is one of the most prestigious universities in Germany. It is a German Excellence University, part of the U15, as well as a founding member of the League of European Research Universities and the Coimbra Group. 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. 57 Nobel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nice
Nice ( ; ) is a city in and the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative city limits, with a population of nearly one millionDemographia: World Urban Areas , Demographia.com, April 2016 on an area of . Located on the French Riviera, the southeastern coast of France on the , at the foot of the French Alps, Nice is the second-largest French city on the Mediterranean coast an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 IMU Abacus Medal (known before 2022 as the Nevanlinna Prize), 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 German mathematicians 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'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University
Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. 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. The institution moved to Newark, New Jersey, Newark in 1747 and then to its Mercer County, New Jersey, Mercer County campus in Princeton nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. 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 instruction in the hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canberra
Canberra ( ; ) is the capital city of Australia. Founded following the Federation of Australia, federation of the colonies of Australia as the seat of government for the new nation, it is Australia's list of cities in Australia, largest inland city, and the list of cities in Australia by population, eighth-largest Australian city by population. 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. Canberra's estimated population was 473,855. The area chosen for the capital had been inhabited by Aboriginal Australians for up to 21,000 years, by groups including the Ngunnawal and Ngambri. history of Australia (1788–1850), European settlement commenced in the first half of the 19th century, as evidenced by surviving landmarks such as St John the Baptist Church, Reid, St John's Anglican Church and Blundells Cottage. On 1 January 1901, federation of the colonies of Australi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Melbourne
Melbourne ( , ; Boonwurrung language, Boonwurrung/ or ) is the List of Australian capital cities, capital and List of cities in Australia by population, most populous city of the States and territories of Australia, Australian state of Victoria (state), Victoria, and the second most-populous city in Australia, after Sydney. The city's name generally refers to a metropolitan area also known as Greater Melbourne, comprising an urban agglomeration of Local Government Areas of Victoria#Municipalities of Greater Melbourne, 31 local government areas. The name is also used to specifically refer to the local government area named City of Melbourne, whose area is centred on the Melbourne central business district and some immediate surrounds. 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 Ranges, and the Macedon R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
