Donald G. Higman (September 20, 1928 in Vancouver – February 13, 2006) was an

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...

mathematician known for his discovery, in collaboration with

Charles C. Sims Charles Coffin Sims (April 14, 1937 – October 23, 2017J. J. O'Connor and E. F. Robertson''Charles Sims biography'' MacTutor History of Mathematics archive. Accessed 2018-12-20.) was an American mathematician best known for his work in group t ...

, of the Higman–Sims group.. Higman did his undergraduate studies at the University of British Columbia, and received his Ph.D. in 1952 from the University of Illinois Urbana-Champaign under Reinhold Baer. 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 In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free modules. Various equivalent characterizati ...

and explained its role in the theory of module decompositions. He developed a characterization of rank-2

permutation group In mathematics, a permutation group is a group ''G'' whose elements are permutations of a given set ''M'' and whose group operation is the composition of permutations in ''G'' (which are thought of as bijective functions from the set ''M'' to it ...

s, and a theory of rank-3 permutation groups; several of the later-discovered

sporadic simple group In mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups. A simple group is a group ''G'' that does not have any normal subgroups except for the trivial group and ''G'' itself. The ...

s were of this type, including the Higman–Sims group which he and Sims constructed in 1967.

References

1928 births 2006 deaths Canadian emigrants to the United States Group theorists University of British Columbia alumni University of Illinois Urbana-Champaign alumni University of Michigan faculty Scientists from Vancouver 20th-century American mathematicians 21st-century American mathematicians {{US-mathematician-stub