Recognition of characteristically simple group $A_5\times A_5$ by character degree graph and order

Abstract

It is shown that finite symmetric groups S n are determined by their complex group algebra, i.e. if G is a finite group with CG ∼ = CS n then it follows that G ∼ = S n .

Recognition of M × M by Its Complex Group Algebra Where M Is a Simple K3-Group

“…is uniquely determined by its complex group algebra, where p ≥ 5 is a prime number (see [19]). In [20], Khosravi and Khademi proved that the characteristically simple group A 5 × A 5 is uniquely determined by its order and its character degree graph (vertices are the prime divisors of the irreducible character degrees of G and two vertices p and q are joined by an edge if pq divides some irreducible character degree of G). In this paper, we prove that if M is a simple K 3 -group, then M × M is uniquely determined by its order and some information about its irreducible character degrees.…”