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.
G. A. Fernández-Alcober, M. Morigi, P. Shumyatsky (2014). Procyclic coverings of commutators in profinite groups. ARCHIV DER MATHEMATIK, 103(2), 101-109 [10.1007/s00013-014-0672-y].
Procyclic coverings of commutators in profinite groups
MORIGI, MARTA;
2014
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
