Quasi –permutation representations of Borel subgroup of Steinbergs triality group s with minimal degree

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 finite group G let Gp denote the minimal degree of a faithful permutation representation of G and let Gq and Gc denote the minimal degree of a faithful representation of G by quasi-permutation matrices over the rationals and the complex numbers respectively. Finally Gr denotes the minimal degree of a faithful rational valued complex character of G. In this paper Gq, Gc and Gr are calculated for the Borel subgroup of Steinbergs triality groups.

کلیدواژه ها:

Borel subgroup ، Character table ، Quasi-permutation representation ، Rational value character ، Steinberg triality group