Ruifang Chen, Xianhe Zhao: On real conjugacy class sizes and the structure of finite groups, 273-278

Abstract:

Let $G$ be a finite group. We prove that if all noncentral primary and biprimary even real classes of $G$ have prime sizes, then $G$ has either a normal $2$-complement or a normal Sylow 2-subgroup.

Key Words: real class, solvable group, normal 2-complement, normal Sylow 2-subgroup.

2010 Mathematics Subject Classification: Primary 20E45; Secondary 20D10.