ON THE CHARACTER DEGREE GRAPH OF THE GROUP SZ(Q), FOR SOME Q

The character degree graph of a finite group G is the graph whose vertices are the prime divisors of the irreducible character degrees of G and two vertices p and p ′ are joined by an edge if pp ′ divides some irreducible character degree of G. In this talk 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.