TY - JOUR
ID - 88262
TI - Groups with Two Extreme Character Degrees and their Minimal Faithful Representations
JO - Mathematics Interdisciplinary Research
JA - MIR
LA - en
SN - 2538-3639
AU - Delfani, Mahtab
AU - Behravesh, Houshang
AD - Department of Mathematics, Urmia University, Urmia, Iran
Y1 - 2018
PY - 2018
VL - 3
IS - 2
SP - 109
EP - 115
KW - quasi-permutation
KW - Linear character
KW - Non-linear character
DO - 10.22052/mir.2019.186347.1133
N2 - 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)):
UR - http://mir.kashanu.ac.ir/article_88262.html
L1 - http://mir.kashanu.ac.ir/article_88262_bbea5fc48f8ecb778827001fced83bbd.pdf
ER -