Procyclic coverings of commutators in profinite groups

被引：0

作者：

Gustavo A. Fernández-Alcober

Marta Morigi

Pavel Shumyatsky

机构：

[1] University of the Basque Country UPV/EHU,Department of Mathematics

[2] Università di Bologna,Dipartimento di Matematica

[3] University of Brasilia,Department of Mathematics

来源：

Archiv der Mathematik | 2014年 / 103卷

关键词：

20E18; 20F14; Profinite groups; Procyclic subgroups; Commutators;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：101 / 109

页数：8

共 8 条

[1] Acciarri C.(2013)On profinite groups in which commutators are covered by finitely many subgroups Math. Z. 274 239-248
[2] Shumyatsky P.(2014)On finite groups in which coprime commutators are covered by few cyclic subgroups J. Algebra 407 358-371
[3] Acciarri C.(2010)Verbal sets and cyclic coverings J. Algebra 324 1616-1624
[4] Shumyatsky P.(1982)Commutators and commutator subgroups Adv. Math. 45 319-330
[5] Cutolo G.(1946)On infinite soluble groups, III Proc. London Math. Soc. 49 184-194
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