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.

6 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 (2)

• Finite and nilpotent strongly verbally closed groups
• Finite normal subgroups of strongly verbally closed groups

Cited by in corpus (1)

• Finite symmetric groups are strongly verbally closed