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

Hung P. Tong-Viet

Vol. 308 (2020), No. 1, 207–222

DOI: 10.2140/pjm.2020.308.207

Abstract

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

Keywords

conjugacy classes, $p$-elements, normal $p$-complements

Mathematical Subject Classification

Primary: 20E45

Secondary: 20D10, 20D20

Milestones

Received: 1 March 2020

Revised: 22 May 2020

Accepted: 28 May 2020

Published: 3 December 2020