Finite and nilpotent strongly verbally closed groups

Abstract

We show, in particular, that, if a finite group $H$ is a retract of any finite group containing $H$ as a verbally closed subgroup, then the centre of $H$ is a direct factor of $H$.

13 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V2: Results concerning strong retracts are improved slightly. V3: minor errors in the last section are corrected. V4: misprints are corrected

Cited by in corpus (3)

• Finite normal subgroups of strongly verbally closed groups
• The centre of a finitely generated strongly verbally closed group is almost always pure
• Finite symmetric groups are strongly verbally closed