If G is a finite linear group of degree n, that is, a finite group of automor-phisms 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. By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace.
Thus every permutation matrix over C is a quasi-permutation matrix. For a given finite group G, let c(G) denote the minimal degree of a faithful rep-resentation of G by quasi-permutation matrices over the complex numbers and let r(G) denote the minimal degree of a faithful rational valued complex character of G. The purpose of this paper is to calculate c(G) and r(G) for
the Borel and parabolic subgroups of Steinberg's triality groups.
Ghorbany,M . (2009). Quasi-permutation Representations of Borel and Parabolic Subgroups of Steinberg's triality groups. (e24406). Iranian Journal of Numerical Analysis and Optimization, 2(1), e24406 doi: 10.22067/ijnao.v2i1.637
MLA
Ghorbany,M . "Quasi-permutation Representations of Borel and Parabolic Subgroups of Steinberg's triality groups" .e24406 , Iranian Journal of Numerical Analysis and Optimization, 2, 1, 2009, e24406. doi: 10.22067/ijnao.v2i1.637
HARVARD
Ghorbany M. (2009). 'Quasi-permutation Representations of Borel and Parabolic Subgroups of Steinberg's triality groups', Iranian Journal of Numerical Analysis and Optimization, 2(1), e24406. doi: 10.22067/ijnao.v2i1.637
CHICAGO
M Ghorbany, "Quasi-permutation Representations of Borel and Parabolic Subgroups of Steinberg's triality groups," Iranian Journal of Numerical Analysis and Optimization, 2 1 (2009): e24406, doi: 10.22067/ijnao.v2i1.637
VANCOUVER
Ghorbany M. Quasi-permutation Representations of Borel and Parabolic Subgroups of Steinberg's triality groups. Iran. J. Numer. Anal. Optim.. 2009;2(1):e24406. doi: 10.22067/ijnao.v2i1.637
