@article {
author = {Akhlaghi, Zeinab and Khatami, Maryam and Khosravi, Behrooz},
title = {Recognition of the simple groups $PSL_2(q)$ by character degree graph and order},
journal = {International Journal of Group Theory},
volume = {8},
number = {2},
pages = {41-46},
year = {2019},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2017.103226.1424},
abstract = {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 $G\cong PSL_2(q)$.},
keywords = {character degree graph,simple group,characterization},
url = {https://ijgt.ui.ac.ir/article_22212.html},
eprint = {https://ijgt.ui.ac.ir/article_22212_c6dca60b79cceb6b7922abee8ca0c87c.pdf}
}