Finite symmetric groups are strongly verbally closed
Group Theory
2025-10-14 v2
Abstract
Answering a question of A. V. Vasil'ev, we show that each finite symmetric (or alternating) group is a retract of any group containing as a verbally closed subgroup.
Cite
@article{arxiv.2405.01179,
title = {Finite symmetric groups are strongly verbally closed},
author = {Olga K. Karimova and Anton A. Klyachko},
journal= {arXiv preprint arXiv:2405.01179},
year = {2025}
}
Comments
4 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V2: An argument is simplified (thanks to A. Yu. Olshanskii)