Graham Higman
Graham Higman ( born January 19, 1917 in Louth in Lincolnshire, † April 8, 2008 in Oxford ) was an English mathematician, algebra, especially group theory, dealt.
Life and work
Higman was the son of a minister and went to school in Plymouth. He then studied with a scholarship at Balliol College, Oxford University in the topologist JHC Whitehead, where he received his doctorate in 1941 with On the units of group rings He then spent a year at Cambridge University in Philip Hall. During the Second World War, worked as a meteorologist in Northern Ireland and Gibraltar (he had to register in advance as a conscientious objector ). In 1946 he went as a lecturer at the University of Manchester to Max Newman. At the same time there were the group theorist Walter Ledermann and Bernhard Neumann. In 1955 he became a lecturer at Oxford, and shortly thereafter Reader. In 1958, he was Senior Research Fellow at Balliol College. 1960-1984 he was the successor of his teacher Whitehead " Waynflete Professor of Pure Mathematics" at Magdalen College, Oxford, which he was a Fellow in 1960. In 1984, he retired in Oxford from 1984 to 1986 and was a professor at the University of Illinois.
Higman made many important contributions to group theory. 1949 ( embedding theorem for groups ) he introduced the HNN - extensions of groups with Bernhard Neumann and Hanna Neumann. In 1956 he wrote with Philip Hall an important work ( On the -length of- soluble groups and reduction theorems for Burnside 's problem-. Proceedings of the London Mathematical Society) over the restricted Burnside problem ( which was dissolved in the 1990s by Zelmanov ). Also be embedding theorem is 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 on the discovered just Zvonimir Janko sporadic simple groups ( he designed together with John McKay ) and also about the Higman - Sims group, but not by him, but by the US- American Donald G. Higman (1928-2006) is named. Although he was 1960/61, at the University of Chicago, where at the time a group theory seminar continued the program classification of finite simple groups in transition, held themselves but off the onset of intensive work on the classification. In 1988 his book with Elizabeth Scott Existentially closed groups ( Clarendon Press, Oxford).
Higman was a member ( "Fellow" ) was added in 1958 to the Royal Society in 1979, the Sylvester Medal awarded him. From 1965 to 1967 he was President of the London Mathematical Society, of which he Berwick Prize in 1962 and the De Morgan Medal he received in 1974. He was the founder of the Journal of Algebra, 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).
For his dissertation, the Isormophismusproblem for group rings originates (for example, over the integers ) and a similar presumption. It was confirmed for some groups ( Klaus W. Roggenkamp, Leonard Scott, 1980 ), but overall refuted ( Martin Hertwick, Stuttgart 2001).
His doctoral include Stephen D. Smith, Peter Neumann and Jonathan Alperin.
1936 to 2001 he was also Methodist preacher in Oxford ( Wesley Memorial Church). He was an avid bird watcher. Higman was married from 1941 to 1981 the death of his wife and had five sons and a daughter.