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arXiv · 2308.06837

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

Filipp D. Denissov·Anton A. Klyachko
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Abstract

The assertion in the title implies that many interesting groups (e.g., all non-abelian braid groups or ${\bf SL}_{100}(\mathbb Z)$) 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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Filipp D. Denissov, Anton A. Klyachko. 2023-08-13. The centre of a finitely generated strongly verbally closed group is almost always pure. https://doi.org/10.1093/qmath%2Fhaae038

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