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- Title
On small profinite groups.
- Authors
Helbig, Patrick
- 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.
- Subjects
PROFINITE groups; FINITE groups; FRATTINI subgroups; MAXIMAL subgroups; LUBOTZKY, Alexander
- Publication
Journal of Group Theory, 2017, Vol 20, Issue 5, p987
- ISSN
1433-5883
- Publication type
Article
- DOI
10.1515/jgth-2017-0014