Recognition by character degree graph and order of simple groups of order less than 6000

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 if G is a simple group of order less that 6000, then G is uniquely determined by its character degree graph and its order. Also by an example we show that this result is not true for all simple groups. © 2014 Miskolc University Press.