Procyclic coverings of commutators in profinite groups

2014/05/21 by Gustavo A. Fernández‐Alcober, Fernández-Alcober, Gustavo A., Marta Morigi +3 · 1 citation
Mathematics · Engineering · Computer Science · #Finite Group Theory Research #graph theory and CDMA systems #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.1405.5352

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.

Cited by

• Coprime commutators in profinite groups

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