Donald G. Higman (September 20, 1928 in

Vancouver Vancouver is a major city in Western Canada, located in the Lower Mainland region of British Columbia. As the List of cities in British Columbia, most populous city in the province, the 2021 Canadian census recorded 662,248 people in the cit ...

– 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, p ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

known for his discovery, in collaboration with Charles C. Sims, of the

Higman–Sims group In the area of modern algebra known as group theory, the Higman–Sims group HS is a sporadic simple group of order : 44,352,000 = 293253711 : ≈ 4. The Schur multiplier has order 2, the outer automorphism group has order 2, an ...

.. Higman did his undergraduate studies at the

University of British Columbia The University of British Columbia (UBC) is a Public university, public research university with campuses near University of British Columbia Vancouver, Vancouver and University of British Columbia Okanagan, Kelowna, in British Columbia, Canada ...

, and received his Ph.D. in 1952 from the

University of Illinois Urbana-Champaign The University of Illinois Urbana-Champaign (UIUC, U of I, Illinois, or University of Illinois) is a public university, public land-grant university, land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United ...

under

Reinhold Baer Reinhold Baer (22 July 1902 – 22 October 1979) was a German mathematician, known for his work in algebra. He introduced injective modules in 1940. He is the eponym of Baer rings, Baer groups, and Baer subplanes. Biography Baer studied mecha ...

. He served on the faculty of mathematics at the

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

from 1956 to 1998. His work on

homological Homology, homologous, homologation or homological may refer to: Sciences Biology *Homology (biology), any characteristic of biological organisms that is derived from a common ancestor *Sequence homology, biological homology between DNA, RNA, ...

aspects of

group representation theory In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to r ...

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 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 ...

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

sporadic simple group In the mathematical classification of finite simple groups, there are a number of groups which do not fit into any infinite family. These are called the sporadic simple groups, or the sporadic finite groups, or just the sporadic groups. A simpl ...

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