Profinite groups with few conjugacy classes of $p$-elements

John S. Wilson

Profinite groups with few conjugacy classes of $p$-elements

Group Theory 2022-09-30 v2

Authors: John S. Wilson

Abstract

It is proved that a profinite group $G$ has fewer than $2^{\aleph_0}$ conjugacy classes of $p$ -elements for an odd prime $p$ if and only if its $p$ -Sylow subgroups are finite. (Here, by a $p$ -element one understands an element that either has $p$ -power order or topologically generates a group isomorphic to ${\mathbb Z}_p$ .) A weaker result is proved for $p=2$ .

Keywords

finite groups conjugacy classes in groups finite group theory

Cite

@article{arxiv.2204.09936,
  title  = {Profinite groups with few conjugacy classes of $p$-elements},
  author = {John S. Wilson},
  journal= {arXiv preprint arXiv:2204.09936},
  year   = {2022}
}

Comments

Corrected version of a paper to appear in Proc. Amer. Math. Soc. (2022), with expanded explanations

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