Finite and nilpotent strongly verbally closed groups
Group Theory
2023-07-17 v4
Abstract
We show, in particular, that, if a finite group is a retract of any finite group containing as a verbally closed subgroup, then the centre of is a direct factor of .
Cite
@article{arxiv.2109.12397,
title = {Finite and nilpotent strongly verbally closed groups},
author = {Anton A. Klyachko and Veronika Yu. Miroshnichenko and Alexander Yu. Olshanskii},
journal= {arXiv preprint arXiv:2109.12397},
year = {2023}
}
Comments
13 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V2: Results concerning strong retracts are improved slightly. V3: minor errors in the last section are corrected. V4: misprints are corrected