%0 Journal Article
%T Recognition of the simple groups $PSL_2(q)$ by character degree graph and order
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Akhlaghi, Zeinab
%A Khatami, Maryam
%A Khosravi, Behrooz
%D 2019
%\ 06/01/2019
%V 8
%N 2
%P 41-46
%! Recognition of the simple groups $PSL_2(q)$ by character degree graph and order
%K character degree graph
%K simple group
%K characterization
%R 10.22108/ijgt.2017.103226.1424
%X Let $G$ be a finite group, and $Irr(G)$ be the set of complex irreducible characters of $G$. Let $\rho(G)$ be the set of prime divisors of character degrees of $G$. The character degree graph of $G$, which is denoted by $\Delta(G)$, is a simple graph with vertex set $\rho(G)$, and we join two vertices $r$ and $s$ by an edge if there exists a character degree of $G$ divisible by $rs$. In this paper, we prove that if $G$ is a finite group such that $\Delta(G)=\Delta(PSL_2(q))$ and $|G|=|PSL_2(q)|$, then $G\cong PSL_2(q)$.
%U https://ijgt.ui.ac.ir/article_22212_c6dca60b79cceb6b7922abee8ca0c87c.pdf