 He served on the faculty of mathematics at the University of Michigan from 1956 to 1998.His work on homological aspects of group representation theory established the concept of a relatively projective module and explained its role in the theory of module decompositions.He developed a characterization of rank-2 permutation groups, and a theory of rank-3 permutation groups; several of the later-discovered sporadic simple groups were of this type, including the Higman–Sims group which he and Sims constructed in 1967.