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arXiv · 2506.20029

Covering the set of $p$-elements in finite groups by Sylow $p$-subgroups

Attila Maróti·Juan Martínez·Alexander Moretó
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Abstract

Let $G_p$ be the set of $p$-elements of a finite group $G$. Do we need all the Sylow $p$-subgroups of $G$ to cover $G_p$? Although this question does not have an affirmative answer in general, our work indicates that the answer is yes more often than one could perhaps expect.

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Attila Maróti, Juan Martínez, Alexander Moretó. 2025-06-24. Covering the set of $p$-elements in finite groups by Sylow $p$-subgroups. https://arxiv.org/abs/2506.20029

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