SOME EXTENSIONS OF PSL(2, p2) ARE UNIQUELY DETERMINED BY THEIR COMPLEX GROUP ALGEBRAS

In Tong-Viet's, 2012 work, the following question arose: Question. Which groups can be uniquely determined by the structure of their complex group algebras? It is proved here that some simple groups of Lie type are determined by the structure of their complex group algebras. Let p be an odd prime number and S = PSL (2, p(2)). In this paper, we prove that, if M is a finite group such that S < M < Aut (S), M = Z(2) x PSL (2, p(2)) or M = SL (2, p(2)), then M is uniquely determined by its order and some information about its character degrees. Let X-1 (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 X-1 (G) = X-1 (M), then G congruent to M. This implies that M is uniquely determined by the structure of its complex group algebra.