Profinite groups with few conjugacy classes of $p$-elements
- Resource Type
- Working Paper
- Authors
- Wilson, John S.
- Source
- Subject
- Mathematics - Group Theory
20E18 (Primary) 20E45, 22C05 (Secondary)
- Language
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 $p=2$.
Comment: Corrected version of a paper to appear in Proc. Amer. Math. Soc. (2022), with expanded explanations