Recognition of the simple group PSL(2, p²) by character degree graph and order

چکیده مقاله

Let G be a finite group. The character degree graph of G, which is denoted by Γ(G), is the graph whose vertices are the prime divisors of the character degrees of the group G and two vertices p₁ and p₂ are joined by an edge if p₁p₂ divides some character degree of G. In this paper we prove that the simple group PSL(2, p²) is uniquely determined by its character degree graph and its order. Let X₁(G) be the set of all irreducible complex character degrees of G counting multiplicities. As a consequence of our results we prove that if G is a finite group such that (Formula Presented/), then G ≅ PSL(2, p²). This implies that PSL(2, p²) is uniquely determined by the structure of its complex group algebra. © 2014, Springer-Verlag Wien.