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On quasi-permutation representations of finite groups

Published online by Cambridge University Press:  18 May 2009

J. M. Burns ,
B. Goldsmith ,
B. Hartley  and
R. Sandling
J. M. Burns
Affiliation:
Department of Mathematics, University College, Galway, Ireland
B. Goldsmith
Affiliation:
Department of Mathematics, Statistics and Computer Science, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland
B. Hartley
Affiliation:
Department of MathematicsUniversity of Manchester, Manchester M13 9PL, England
R. Sandling
Affiliation:
Department of MathematicsUniversity of Manchester, Manchester M13 9PL, England
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In [6], Wong defined a quasi-permutation group of degree n to be a finite group G of automorphisms of an n-dimensional complex vector space such that every element of G has non-negative integral trace. The terminology derives from the fact that if G is a finite group of permutations of a set ω of size n, and we think of G as acting on the complex vector space with basis ω, then the trace of an element g ∈ G is equal to the number of points of ω fixed by g. In [6] and [7], Wong studied the extent to which some facts about permutation groups generalize to the quasi-permutation group situation. Here we investigate further the analogy between permutation groups and quasipermutation groups by studying the relation between the minimal degree of a faithful permutation representation of a given finite group G and the minimal degree of a faithful quasi-permutation representation. We shall often prefer to work over the rational field rather than the complex field.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 3 , September 1994 , pp. 301 - 308
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

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