%0 Journal Article
%T Groups with Two Extreme Character Degrees and their Minimal Faithful Representations
%J Mathematics Interdisciplinary Research
%I University of Kashan
%Z 2538-3639
%A Delfani, Mahtab
%A Behravesh, Houshang
%D 2018
%\ 12/01/2018
%V 3
%N 2
%P 109-115
%! Groups with Two Extreme Character Degrees and their Minimal Faithful Representations
%K quasi-permutation
%K Linear character
%K Non-linear character
%R 10.22052/mir.2019.186347.1133
%X for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will show that c(G)≤ |G : Z(G)|^{1/2} c(Z(G)) , p(G) ≤ |G : Z(G)|^{1/2}p(Z(G)):
%U http://mir.kashanu.ac.ir/article_88262_bbea5fc48f8ecb778827001fced83bbd.pdf