Donald G. Higman
Donald Gordon Higman (born September 20, 1928 in Vancouver , † February 13, 2006 ) was an American mathematician who dealt with finite groups, representation theory of groups, combinatorics and geometric applications of groups.
Higman studied at the University of British Columbia and received his doctorate in 1952 from the University of Illinois at Urbana-Champaign with Reinhold Baer (Focal Series in Finite Groups). As a post-doc he spent two years at McGill University with Hans Zassenhaus and at Montana State University . From 1956 he was an assistant professor at the University of Michigan , where he became a professor in 1960 and retired in 1998.
With Charles Sims he discovered the Higman Sims group, a sporadic group . The two mathematicians also found a representation in the automorphism group of a regular graph with 100 vertices and 1100 edges, the Higman-Sims graph. The construction arose from Higman's theory of the rank 3 permutation groups. With this theory, Jack E. McLaughlin , a colleague at the University of Michigan with whom Higman worked a lot, constructed another sporadic group in 1968.
In representation theory, he introduced the concept of the relatively projective module of group algebra of a finite group, for which he specified a criterion named after him. Independently of Gerhard Hochschild , he developed a theory of relatively homological algebras.
In 1970 he introduced the concept of coherent configurations in combinatorics, an axiomatization of the structure of permutation groups in a combinatorial environment, arose from his concern with the combinatorial structure of permutation groups in the 1960s. In the 1980s and 1990s, he applied the concept to geometric issues. In 1970 he was invited speaker at the International Congress of Mathematicians in Nice ( A survey about some questions and results about rank 3 permutation groups ).
He should not be confused with Graham Higman , who also worked on finite groups (and even the Higman-Sims group).
Web links
- List of publications , with an essay by Eiichi Bannai, Robert Griess , Cheryl Praeger , Leonard Scott The mathematics of Donald Gordon Higman , Michigan Math. Journal Vol. 58, 2009
- Literature by and about Donald G. Higman in the WorldCat bibliographic database
Individual evidence
- ^ Higman, Sims A simple group of order 44.352.000 , Mathematische Zeitschrift, Vol. 105, 1968, p. 110
- ^ Higman-Sims-Graph at Math World
- ↑ Higman Finite permutation groups of rank 3 , Mathematische Zeitschrift, Vol. 86, 1964, pp. 145-156
- ^ Higman Modules with a group of operators , Duke Mathematical Journal, Vol. 21, 1954, p. 369
- ↑ Higman Coherent configurations , part 1, rend. Mat. Sem. Univ. Padova, Vol. 44, 1970, pp. 1-25
| personal data | |
|---|---|
| SURNAME | Higman, Donald |
| ALTERNATIVE NAMES | Higman, Donald Gordon; Higman, Donald G. |
| BRIEF DESCRIPTION | American mathematician |
| DATE OF BIRTH | September 20, 1928 |
| PLACE OF BIRTH | Vancouver |
| DATE OF DEATH | February 13, 2006 |