Finite normal subgroups of strongly verbally closed groups
Group Theory
2024-02-16 v2
Abstract
In the recent paper by A. A. Klyachko, V. Yu. Miroshnichenko, and A. Yu. Olshanskii, it is proven that the center of any finite strongly verbally closed group is its direct factor. One of the results of the current paper is the generalization of this nontrivial fact to the case of finite normal subgroups of any strongly verbally closed groups. It follows from this generalization that finitely generated nilpotent groups with nonabelian torsion subgroups are not strongly verbally closed.
Keywords
Cite
@article{arxiv.2301.02752,
title = {Finite normal subgroups of strongly verbally closed groups},
author = {Filipp D. Denissov},
journal= {arXiv preprint arXiv:2301.02752},
year = {2024}
}
Comments
11 pages. V2: Proposition concerning the center of a strong retract is added, and minor errors are corrected