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The minimal degree of a faithful quasi-permutation representation of an abelian group

Published online by Cambridge University Press:  18 May 2009

Houshang Behravesh
Houshang Behravesh
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, England
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Let G be a finite linear group of degree n; that is, a finite group of automorphisms of an n-dimensional complex vector space (or, equivalently, a finite group of non-singular matrices of order n with complex coefficients). We shall say that G is a quasi-permutation group if the trace of every element of G is a non-negative rational integer. The reason for this terminology is that, if G is a permutation group of degree n, its elements, considered as acting on the elements of a basis of an n -dimensional complex vector space V, induce automorphisms of V forming a group isomorphic to G. The trace of the automorphism corresponding to an element x of G is equal to the number of letters left fixed by x, and so is a non-negative integer. Thus, a permutation group of degree n has a representation as a quasi-permutation group of degree n. See [5].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 1 , January 1997 , pp. 51 - 57
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

REFERENCES

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