Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-14T22:30:39.137Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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.

Information

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

References

REFERENCES

1.Cannon, J. J., An introduction to the group theory language, Cayley, Computational group theory, 145–183 (Academic Press, London, 1984).Google Scholar
2.Dornhoff, L., Group representation theory, Part A (Marcel Dekker, New York, 1971).Google Scholar
3.Hoffman, M., An invariant of finite abelian groups, Amer. Math. Monthly 94 (1987), 664–666.CrossRefGoogle Scholar
4.Isaacs, I. M., Character theory of finite groups (Academic Press, New York, 1976).Google Scholar
5.Shojaei, M. A. Shahabi, Schur indices of irreducible characters of SL(2, q), Arch. Math. 40 (1983), 221–231.CrossRefGoogle Scholar
6.Wong, W. J., Linear groups analogous to permutation groups. J. Austral. Math. Soc. (Sec. A) 3 (1963), 180–184.CrossRefGoogle Scholar
7.Wong, W. J., On linear p-groups, J. Austral. Math. Soc. (Ser. A) 4 (1964), 174–178.CrossRefGoogle Scholar