Virtually free finite-normal-subgroup-free groups are strongly verbally closed

Abstract

Any virtually free group $H$ containing no non-trivial finite normal subgroup (e.g., the infinite dihedral group) is a retract of any finitely generated group containing $H$ as a verbally closed subgroup.

arXiv comment6 pages. V2: minor corrections. V3: misprint corrections. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm

References in corpus (1)

• Verbally closed virtually free subgroups

Cited by in corpus (6)

• Finite and nilpotent strongly verbally closed groups
• The Klein bottle group is not strongly verbally closed, though awfully close to being so
• Finite normal subgroups of strongly verbally closed groups
• Free products of groups are strongly verbally closed
• The centre of a finitely generated strongly verbally closed group is almost always pure
• Finite symmetric groups are strongly verbally closed