Submission date: 3 June 2020

Abstract:

We prove that if a countable group is elementarily equivalent to a non-abelian free group and all of its finitely generated abelian subgroups are cyclic, then the group is a union of a chain of regular NTQ groups (i.e., hyperbolic towers).

Mathematics Subject Classification: 03C60, 20E05, 20F70

Keywords and phrases:

Full text (arXiv 2006.02414: pdf, ps.