Khatami, M., Akhlaghi, Z., Khosravi, B. (2017). Recognition of the simple groups $PSL_2(q)$ by character degree graph and order. International Journal of Group Theory, (), -. doi: 10.22108/ijgt.2017.103226.1424

Maryam Khatami; Zeinab Akhlaghi; Behrooz Khosravi. "Recognition of the simple groups $PSL_2(q)$ by character degree graph and order". International Journal of Group Theory, , , 2017, -. doi: 10.22108/ijgt.2017.103226.1424

Khatami, M., Akhlaghi, Z., Khosravi, B. (2017). 'Recognition of the simple groups $PSL_2(q)$ by character degree graph and order', International Journal of Group Theory, (), pp. -. doi: 10.22108/ijgt.2017.103226.1424

Khatami, M., Akhlaghi, Z., Khosravi, B. Recognition of the simple groups $PSL_2(q)$ by character degree graph and order. International Journal of Group Theory, 2017; (): -. doi: 10.22108/ijgt.2017.103226.1424

Recognition of the simple groups $PSL_2(q)$ by character degree graph and order

^{1}Faculty of Mathematics and Computer science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

^{2}Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15914 Tehran, Iran

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 $G \cong PSL_2(q)$.