The centre of a finitely generated strongly verbally closed group is almost always pure

ABSTRACT The assertion in the title implies that many interesting groups (for example, all non-abelian braid groups or $\textbf{SL}_{100}(\mathbb{Z})$) are not strongly verbally closed, i. e., they embed into some finitely generated groups as verbally closed subgroups, which are not retracts.

Saved in:
Bibliographic Details
Published in:Quarterly journal of mathematics 2024-08, Vol.75 (3), p.1149-1156
Main Authors: Denissov, Filipp D, Klyachko, Anton A
Format: Article
Language:English
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:ABSTRACT The assertion in the title implies that many interesting groups (for example, all non-abelian braid groups or $\textbf{SL}_{100}(\mathbb{Z})$) are not strongly verbally closed, i. e., they embed into some finitely generated groups as verbally closed subgroups, which are not retracts.
ISSN:0033-5606
1464-3847
DOI:10.1093/qmath/haae038