Geodesic
The minimal degree of a faithful quasi-permutation representation of an abelian group
Glasgow mathematical journal, Tome 39 (1997) no. 1, pp. 51-57

Voir la notice de l'article provenant de la source Cambridge University Press

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]. 
Behravesh, Houshang. The minimal degree of a faithful quasi-permutation representation of an abelian group. Glasgow mathematical journal, Tome 39 (1997) no. 1, pp. 51-57. doi: 10.1017/S0017089500031906
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[1] 1.Burns, J. M., Goldsmith, B., Hartley, B. and Sandling, R., On quasi-permutation representations of finite groups, Glasgow Math. J. 36 (1994), 301–308. Google Scholar | DOI

[2] 2.Hoffman, M., An invariant of finite abelian groups. Amer. Math. Monthly 94 (1987), 664–666. Google Scholar | DOI

[3] 3.Isaacs, I. M., Character theory of finite groups (Academic Press, New York, 1976). Google Scholar

[4] 4.Sehgal, S. K., Topics in group rings (Marcel Dekker, New York, 1978). Google Scholar

[5] 5.Wong, W. J., Linear groups analogous to permutation groups, J. Austral. Math. Soc. Ser. A 3 (1963), 180–184. Google Scholar | DOI

[6] 6.Wong, W. J., On linear p-groups, J. Austral. Math. Soc. Ser. A 4 (1964), 174–178. Google Scholar | DOI

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