Embeddings of finite projective general linear groups

A square matrix over the complex field with non-negative integral trace is called a quasipermutation matrix. Thus , every permutation matrix over C is a quasi-permutation matrix. For a given finite group G , let p(G) denote the minimal degree of a faithful permutation representation of G . The minimal degree of a faithful representation of G by quasi-permutation matrices over the rational and the complex numbers are denoted by q(G) and c(G) respectively. Finally r(G) denotes the minimal degree of a faithful rational valued complex character of G . In this paper we will calculate p(G), q(G), c(G) and r(G) for the finite projective general linear groups.

کلیدواژه ها:

Character table ، Quasi-permutation representation ، Projective general linear group