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Special Properties of the Linear Group GL(3, q)

Ghorbany M. نويسنده

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A square matrix over F with non-negative integral trace is called a quasipermutation matrix over F. Let G be a finite linear group of degree n, that is, a finite group of authomorphisms 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. Thus a permutation group of degree n has a representation as a quasi-permutation group of degree n.ln this paper we calculate the kernel and Galois groups for the irreducible characters of the group GL(3, q). These help us to obtain the permutation and quasi-permutation representations of the group GL(3, q) .

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