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.

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Published in:Quarterly journal of mathematics 2024-08, Vol.75 (3), p.1149-1156
Main Authors: Denissov, Filipp D, Klyachko, Anton A
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description 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.
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title The centre of a finitely generated strongly verbally closed group is almost always pure
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