Recognition of characteristically simple group by character degree graph and order
The character degree graph of a finite group is the graph whose vertices are the prime divisors of the irreducible character degrees of and two vertices and are joined by an edge if divides some irreducible character degree of . It is proved that some simple groups are uniquely determined by their orders and their character degree graphs. But since the character degree graphs of the characteristically simple groups are complete, there are very narrow class of characteristically simple...