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 (e.g., all non-abelian braid groups or ${\mathbf{SL}}_{100}(\mathbb{Z})$) are not strongly verbally closed, i.e., they embed into some finitely generated groups as verbally closed subgroups, which are not retracts.

arXiv comment6 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V4: minor misprint corrections

References in corpus (6)

• Verbally closed virtually free subgroups
• Virtually free finite-normal-subgroup-free groups are strongly verbally closed
• Finite and nilpotent strongly verbally closed groups
• The Klein bottle group is not strongly verbally closed, though awfully close to being so
• Free products of groups are strongly verbally closed
• Finite normal subgroups of strongly verbally closed groups

Cited by in corpus (1)

• Finite symmetric groups are strongly verbally closed