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arXiv · 1405.5352

Procyclic coverings of commutators in profinite groups

Gustavo A. Fernández-Alcober·Marta Morigi·Pavel Shumyatsky
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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.

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Gustavo A. Fernández-Alcober, Marta Morigi, Pavel Shumyatsky. 2014-05-21. Procyclic coverings of commutators in profinite groups. https://arxiv.org/abs/1405.5352

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