Procyclic coverings of commutators in profinite groups
Group Theory
2014-05-22 v1
Abstract
We consider profinite groups in which all commutators are contained in a union of finitely many procyclic subgroups. It is shown that if G is a profinite group in which all commutators are covered by m procyclic subgroups, then G possesses a finite characteristic subgroup M contained in G' such that the order of M is m-bounded and G'/M is procyclic. If G is a pro-p group such that all commutators in G are covered by m procyclic subgroups, then G' is either finite of m-bounded order or procyclic.
Keywords
Cite
@article{arxiv.1405.5352,
title = {Procyclic coverings of commutators in profinite groups},
author = {Gustavo A. Fernández-Alcober and Marta Morigi and Pavel Shumyatsky},
journal= {arXiv preprint arXiv:1405.5352},
year = {2014}
}