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On countable elementary free groups

Published 3 Jun 2020 in math.LO and math.GR | (2006.02414v2)

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

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