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arXiv · 2207.04988

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

N. N. Hung·A. Maróti·J. Martínez
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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 $G$.

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N. N. Hung, A. Maróti, J. Martínez. 2022-10-15. Conjugacy classes of $π$-elements and nilpotent/abelian Hall $π$-subgroups. https://doi.org/10.2140/pjm.2023.323.185

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