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Conjugacy classes of $\pi$-elements and nilpotent/abelian Hall $\pi$-subgroups

Nguyen N. Hung, Attila Maróti and Juan Martínez

Vol. 323 (2023), No. 1, 185–204
DOI: 10.2140/pjm.2023.323.185
Abstract

Let G be a finite group and π be a set of primes. We study finite groups with a large number of conjugacy classes of π-elements. In particular, we obtain precise lower bounds for this number in terms of the π-part of the order of G to ensure the existence of a nilpotent or abelian Hall π-subgroup in G.

Keywords
finite groups, conjugacy classes, $\pi$-elements, Hall subgroups.
Mathematical Subject Classification
Primary: 20E45
Secondary: 20D10, 20D20
Milestones
Received: 18 July 2022
Accepted: 15 October 2022
Published: 29 May 2023
Authors
Nguyen N. Hung
Department of Mathematics
Buchtel College of Arts and Sciences
The University of Akron
Akron, OH
United States
Attila Maróti
Hungarian Academy of Sciences
Alfréd Rényi Institute of Mathematics
Budapest
Hungary
Juan Martínez
Departament de Matemàtiques
Universitat de València
València
Spain

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