Finite normal subgroups of strongly verbally closed groups

Abstract

In the recent paper by A. A. Klyachko, V. Yu. Miroshnichenko, and A. Yu. Olshanskii, it is proven that the center of any finite strongly verbally closed group is its direct factor. One of the results of the current paper is the generalization of this nontrivial fact to the case of finite normal subgroups of any strongly verbally closed groups. It follows from this generalization that finitely generated nilpotent groups with nonabelian torsion subgroups are not strongly verbally closed.

11 pages. V2: Proposition concerning the center of a strong retract is added, and minor errors are corrected

References in corpus (2)

• Finite and nilpotent strongly verbally closed groups
• The Klein bottle group is not strongly verbally closed, though awfully close to being so

Cited by in corpus (2)

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