Profinite groups with few conjugacy classes of p-elements

2022/04/21 by John S. Wilson, Wilson, John S.
Mathematics · Biochemistry, Genetics and Molecular Biology · #Finite Group Theory Research #Rings, Modules, and Algebras #Protein Tyrosine Phosphatases

paper · pdf · doi:10.48550/arxiv.2204.09936

Abstract

It is proved that a profinite group G has fewer than 2^ℵ₀ 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.

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