Donald G. Higman

Donald Gordon Higman ( born September 20, 1928 in Vancouver, † 13 February 2006) was an American mathematician who worked on 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 at the University of Illinois at Urbana -Champaign in Reinhold Baer ( Focal Series in Finite Groups). As a post-doc, he spent two years at McGill University under Hans Zassenhaus and at Montana State University. From 1956 he was assistant professor at the University of Michigan, where he became professor in 1960 and emeritus in 1998.

With Charles Sims, he discovered the Higman - Sims group, a sporadic group. They also found a presentation in the automorphism group of a regular graph with 100 vertices and 1100 edges, the Higman - Sims graph. The design originated from Higman 's theory of permutation groups of rank 3.With this theory constructed Jack E. McLaughlin, a colleague at the University of Michigan with the Higman much worked, in 1968 a further sporadic group.

In the representation theory he introduced the concept of relative - projective module ( Relatively projective modules ) of the group algebra of a finite group for which he gave a criterion named after him. Regardless of Gerhard Hochschild, he developed a theory of relative homological algebra.

In combinatorics, he led in 1970 the concept of a coherent configurations (Coherent Configurations ), an axiomatization of the structure of permutation groups in combinatorial environment, arising from his employment with the combinatorial structure of permutation groups in the 1960s. In the 1980s and 1990s, he turned the concept on geometric questions. In 1970 he was invited speaker at the International Congress of Mathematicians in Nice (A survey aboutsome questions and results about rank 3 permutation groups).

He should not be confused with Graham Higman, who also worked on finite groups (and even on the Higman - Sims group).