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Conjugacy classes of
$\pi$-elements and nilpotent/abelian Hall $\pi$-subgroups
Nguyen N. Hung, Attila Maróti and Juan Martínez |
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Vol. 323 (2023), No. 1, 185–204
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DOI: 10.2140/pjm.2023.323.185
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Abstract |
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Let be a finite group and be a set of primes. We study finite groups with a large number of conjugacy classes of -elements. In particular, we obtain precise lower bounds for this number in terms of the -part of the order of to ensure the existence of a nilpotent or abelian Hall -subgroup in . |
Keywords
finite groups, conjugacy classes, $\pi$-elements, Hall
subgroups.
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Mathematical Subject Classification
Primary: 20E45
Secondary: 20D10, 20D20
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Milestones
Received: 18 July 2022
Accepted: 15 October 2022
Published: 29 May 2023
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Authors |
| Nguyen N. Hung | |
| Department of Mathematics Buchtel College of Arts and Sciences The University of Akron Akron, OH United States |
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| Attila Maróti | |
| Hungarian Academy of Sciences Alfréd Rényi Institute of Mathematics Budapest Hungary |
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| Juan Martínez | |
| Departament de Matemàtiques Universitat de València València Spain |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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