Remarks on profinite groups having few open subgroups
Group Theory
2021-03-31 v3
Abstract
Examples are given of profinite groups that are not strongly complete, and have other `bad' properties, yet have only finitely many open subgroups of each finite index. It is shown that a profinite group with the latter property must be finite if it has finite exponent. The problem of characterizing strongly complete groups in terms of their power subgroups is discussed.
Keywords
Cite
@article{arxiv.1304.3893,
title = {Remarks on profinite groups having few open subgroups},
author = {Dan Segal},
journal= {arXiv preprint arXiv:1304.3893},
year = {2021}
}
Comments
The paper has been rewritten and expanded, with some new material. Similar examples appear in N. Nikolov: Algebraic properties of profinite groups, arXiv:1108.5130 and in the earlier versions of this note