Finite groups whose real classes have prime-power size

Abstract

We present a characterization of the finite groups in which all real classes have prime powers size.If p is a prime, we denote by p * a generic positive integer that is a power of p.Lemma 2.5. Let be H > 1 and M a faithful GF (q)H-module, with q an odd prime. Suppose that ( * ) holds for HM . If v ∈ M # is real in HM , then C H (v) ∈ Hall 2 ′ (H).