The Lengths of Certain Real Conjugacy Classes and the Related Prime Graph

Abstract

Let G be a finite group. In this paper, we study how certain arithmetical conditions on the conjugacy class lengths of real elements of G influence the structure of G. In particular, a new type of prime graph is introduced and studied. We obtain a series of theorems which generalize some existed results.

Keywords

• real elements
• primary elements
• conjugacy class lengths
• prime graph
• <b>P</b>-groups