Conjugacy classes of $p$-elements and normal $p$-complements

Abstract

In this paper, we study the structure of finite groups with a large number of conjugacy classes of $p$-elements for some prime $p$. As consequences, we obtain some new criteria for the existence of normal $p$-complements in finite groups.

Cited by in corpus (2)

• Conjugacy classes of $\pi$-elements and nilpotent/abelian Hall $\pi$-subgroups
• Extremely closed subgroups and a variant on Glauberman's $Z^{\ast }$-theorem