On profinite groups with commutators covered by nilpotent subgroups
Group Theory
2015-01-13 v1
Abstract
Let G be a profinite group. The following results are proved. 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 commutators in G is covered by countably many nilpotent subgroups.
Cite
@article{arxiv.1501.02734,
title = {On profinite groups with commutators covered by nilpotent subgroups},
author = {Pavel Shumyatsky},
journal= {arXiv preprint arXiv:1501.02734},
year = {2015}
}