QUASI-PERMUTATION REPRESENTATIONS OF SUZtTKI GROUP

Abstract

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 quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a faithful representation of G by quasi-permuation matrices over the rational field Q, and let c(G) be the minimal degree of a faithful representation of G by complex quasi-permuatation matrices. Let r(G) denote the minimal degree of a faithful rational valued character of G. In this paper we will calculate c(G), q(G), p(G) and r(G) where G= Sz(q) is the Suzuki group . Also we will show that lim .