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 ...

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 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 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 ...

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 ...

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 ...

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 ...

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.

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

Biography

See also

References