Graham Higman

Graham Higman (born January 19, 1917 in Louth in Lincolnshire , † April 8, 2008 in Oxford ) was an English mathematician who dealt with algebra , especially group theory.

Graham Higman 1960

Live and act

Higman was the son of a minister and went to school in Plymouth . He then studied with a scholarship at Balliol College of Oxford University in the topologists JHC Whitehead , where he in 1941 with The Units of Group-ring received his doctorate. He then spent a year at Cambridge University with Philip Hall . During the Second World War he worked as a meteorologist in Northern Ireland and Gibraltar (he had previously registered as a conscientious objector). In 1946 he went to the University of Manchester as a lecturer to Max Newman . At the same time, the group theorists Walter Ledermann and Bernhard Neumann were there . In 1955 he became a lecturer at Oxford and shortly afterwards a reader. In 1958 he became a Senior Research Fellow at Balliol College. From 1960 to 1984 he was the successor of his teacher Whitehead "Waynflete Professor of Pure Mathematics" at Magdalen College in Oxford , where he became a fellow in 1960. In 1984 he retired from Oxford and was professor at the University of Illinois from 1984 to 1986 .

Higman made many important contributions to group theory. In 1949 ( Embedding theorem for groups ) he introduced the HNN extensions of groups with Bernhard Neumann and Hanna Neumann . In 1956 he wrote an important paper with Philip Hall ( On the -length of -soluble groups and reduction theorems for Burnside's problem ${\displaystyle p}$ ${\displaystyle p}$ . Proceedings London Mathematical Society) on the limited Burnside problem (which was solved by Zelmanov in the 1990s). His embedding theorem is also known: A finitely generated group can be embedded in a finitely presented group if and only if it can be presented recursively. In the 1960s he worked over the straight from Zvonimir Janko discovered sporadic simple groups (he designed with John McKay) and also about the Higman-Sims group, but not for him, but according to the American Donald G. Higman (1928-2006) is named. Although he was at the University of Chicago in 1960/61, where a group theory seminar started the classification program for finite simple groups at the time, he kept himself apart from the intensive work on classification. In 1988 his book was published with Elizabeth Scott Existentially closed groups (Clarendon Press, Oxford). ${\displaystyle J_{3}}$

Higman was accepted as a member (" Fellow ") in the Royal Society in 1958 , which in 1979 awarded him the New Year's Eve Medal . From 1965 to 1967 he was President of the London Mathematical Society , whose Berwick Prize he received in 1962 and whose De Morgan Medal he received in 1974. He was the founder of the Journal of Algebra , of which he was editor from 1964 to 1984. In 1958 he was invited speaker at the International Congress of Mathematicians in Edinburgh (Lie ring methods in the theory of finite nilpotent groups).

The isormophism problem for group rings (for example over the whole numbers) and a corresponding conjecture comes from his dissertation. It has been confirmed for some groups ( Klaus W. Roggenkamp , Leonard Scott , 1980s), but disproved overall ( Martin Hertweck , Stuttgart 2001).

His PhD students include Stephen D. Smith , Peter Neumann , John Mackintosh Howie, and Jonathan Alperin .

From 1936 to 2001 he was also a Methodist preacher in Oxford (Wesley Memorial Church). He was an avid bird watcher. Higman was married from 1941 until his wife's death in 1981 and had five sons and a daughter.

Supporting documents and comments

1. ↑ published in: Proceedings of the London Mathematical Society . Series 2, Vol. 46, No. 1, 1940, pp. 231-248, doi : 10.1112 / plms / s2-46.1.231 .
2. ^ Subgroups of finitely presented groups. In: Proceedings of the Royal Society of London . Series A: Mathematical and Physical Sciences. Vol. 262, No. 1311, 1961, pp. 455-475, JSTOR 2414348 .
3. ↑ This means a finite number of generators and relations between them
4. ↑ Nothing could be found out about a relatives when they met in 1966, but his ancestors came from the same area in Cornwall
5. ↑ entry on Higman; Graham in the Archives of the Royal Society , London

Web links

• John J. O'Connor, Edmund F. Robertson :  Graham Higman. In: MacTutor History of Mathematics archive .
• Obituary in the Independent
• Obituary in the telegraph