Recognition of the simple groups psl2(q) by character degree graph and order

Abstract

Abstract. Let G be a finite group, and Irr(G) be the set of complex irreducible characters of G. Let A.(G) be the set of prime divisors of character degrees of G. The character degree graph of G, which is denoted by δ(G), is a simple graph with vertex set A.(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 δ(G) = δ(PSL2(q)) and |G| = |PSL2(q)|, then G = PSL2(q). © 2019 University of Isfahan.