Recognition of the simple group Sz(q), for some q by character degree graph and order [Articol]

Abstract

Let G be a finite group. The character degree graph of G, which is denoted by ?(G), is the graph whose vertices are the prime divisors of the irreducible character degrees of G and two vertices p and p0 are joined by an edge if pp0 divides some irreducible character degree of G. In this paper, we prove that the simple group Sz(q), for some q, is uniquely determined by its character degree graph and its order. This implies that Sz(q) is uniquely determined by the structure of its complex group algebra.