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.

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

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