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Procyclic coverings of commutators in profinite groups |
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| Authors: | Gustavo A Fernández-Alcober Marta Morigi Pavel Shumyatsky |
| Institution: | 1. Department of Mathematics, University of the Basque Country UPV/EHU, 48080, Bilbao, Spain 2. Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126, Bologna, Italy 3. Department of Mathematics, University of Brasilia, Brasília-DF, 70910-900, Brazil |
| 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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