Revista Matemática Iberoamericana


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Volume 32, Issue 4, 2016, pp. 1331–1339
DOI: 10.4171/RMI/919

Published online: 2016-12-16

On profinite groups with commutators covered by nilpotent subgroups

Pavel Shumyatsky[1]

(1) Universidade de Brasília, Brasilia, Brazil

The following results about a profinite group $G$ are obtained. The commutator subgroup $G’$ is finite if and only if $G$ is covered by countably many abelian subgroups. The group $G$ is finite-by-nilpotent if and only if $G$ is covered by countably many nilpotent subgroups. The main result is that the commutator subgroup $G’$ is finite-by-nilpotent if and only if the set of all commutators in $G$ is covered by countably many nilpotent subgroups.

Keywords: Profinite groups, nilpotent subgroups, commutators

Shumyatsky Pavel: On profinite groups with commutators covered by nilpotent subgroups. Rev. Mat. Iberoam. 32 (2016), 1331-1339. doi: 10.4171/RMI/919