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

Attila Maróti; Juan Martínez; Alexander Moretó

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

Group Theory 2025-06-26 v1

Authors: Attila Maróti , Juan Martínez , Alexander Moretó

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.

Keywords

finite groups Sylow p-subgroups p-elements covering group theory

Cite

@article{arxiv.2506.20029,
  title  = {Covering the set of $p$-elements in finite groups by Sylow $p$-subgroups},
  author = {Attila Maróti and Juan Martínez and Alexander Moretó},
  journal= {arXiv preprint arXiv:2506.20029},
  year   = {2025}
}

Comments

We fix two gaps pointed out by Gunter Malle in the proofs of Theorem D and Theorem 5.1 of the published version

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

Abstract

Keywords

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