English

On verbal subgroups in finite and profinite groups

Group Theory 2017-03-06 v1

Abstract

Let ww be a multilinear commutator word. In the present paper we describe recent results that show that if GG is a profinite group in which all ww-values are contained in a union of finitely (or in some cases countably) many subgroups with a prescribed property, then the verbal subgroup w(G)w(G) has the same property as well. In particular, we show this in the case where the subgroups are periodic or of finite rank.

Keywords

Cite

@article{arxiv.1703.00979,
  title  = {On verbal subgroups in finite and profinite groups},
  author = {Cristina Acciarri and Pavel Shumyatsky},
  journal= {arXiv preprint arXiv:1703.00979},
  year   = {2017}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1112.5879

R2 v1 2026-06-22T18:34:13.295Z