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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G. A. Fernández-Alcober and M. Morigi are supported by the Spanish Government, Grant MTM2011-28229-C02-02. G. A. Fernández-Alcober and P. Shumyatsky are supported by the Brazilian and Spanish Governments, under the project with the following references: Capes/DGU 304/13; PHB2012-0217-PC. G. A. Fernández-Alcober is also supported by the Basque Government, Grant IT753-13. M. Morigi is also supported by INDAM (GNSAGA).
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Fernández-Alcober, G.A., Morigi, M. & Shumyatsky, P. Procyclic coverings of commutators in profinite groups. Arch. Math. 103, 101–109 (2014). https://doi.org/10.1007/s00013-014-0672-y
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DOI: https://doi.org/10.1007/s00013-014-0672-y