On small profinite groups
Group Theory
2015-12-29 v2 Logic
Abstract
A profinite group is called small if it has only finitely many open subgroups of index n for each positive integer n. We show that every Frattini cover of a small profinite group is small. A profinite group is called strongly complete if every subgroup of finite index is open. We show that two profinite groups that are elementarily equivalent, in the first-order language of groups, are isomorphic if one of them is strongly complete, extending a result of Moshe Jarden and Alexander Lubotzky which treats the case of finitely generated profinite groups.
Cite
@article{arxiv.1511.08760,
title = {On small profinite groups},
author = {Patrick Helbig},
journal= {arXiv preprint arXiv:1511.08760},
year = {2015}
}
Comments
Previously titled "Small profinite groups and their elementary theory"; extended Question 3.15