RECOGNITION OF THE SIMPLE GROUPS PSL2(q) BY CHARACTER DEGREE GRAPH AND ORDER

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(PSL2(q)) and vertical bar G vertical bar = vertical bar PSL2(q)vertical bar, then G congruent to PSL2(q).