Verbally closed virtually free subgroups

Abstract

A theorem of Myasnikov and Roman'kov says that any verbally closed subgroup of a finitely generated free group is a retract. We prove that all free (and many virtually free) verbally closed subgroups are retracts in any finitely generated group.

5 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V.5: An error in an example is corrected (Section 2); thanks to Mikhail Mikheenko

Cited by in corpus (4)

• 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
• The centre of a finitely generated strongly verbally closed group is almost always pure