Donald G. Higman
Encyclopedia
Donald G. Higman was an American
mathematician
known for his discovery, in collaboration with Charles C. Sims, 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
and explained its role in the theory of module decompositions.
He developed a characterization of rank-2 permutation group
s, 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.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
known for his discovery, in collaboration with Charles C. Sims, of the Higman–Sims group.
Higman did his undergraduate studies at the University of British Columbia
University of British Columbia
The University of British Columbia is a public research university. UBC’s two main campuses are situated in Vancouver and in Kelowna in the Okanagan Valley...
, and received his Ph.D. in 1952 from the University of Illinois Urbana-Champaign under Reinhold Baer
Reinhold Baer
Reinhold Baer was a German mathematician, known for his work in algebra. He introduced injective modules in 1940. He is the eponym of Baer rings....
. He served on the faculty of mathematics at the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
from 1956 to 1998.
His work on homological aspects of group representation theory
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
established the concept of a relatively projective module
Projective module
In mathematics, particularly in abstract algebra and homological algebra, the concept of projective module over a ring R is a more flexible generalisation of the idea of a free module...
and explained its role in the theory of module decompositions.
He developed a characterization of rank-2 permutation group
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 ; the relationship is often written as...
s, 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.