Independence property and hyperbolic groups

Abstract

We prove that existentially closed $CSA$-groups have the independence property. This is done by showing that there exist words having the independence property relatively to the class of torsion-free hyperbolic groups.

v3: 10 pages (11pt), a few typos corrected, minor rearrangements (e.g. Fact 2.3 and Lemma 2.5); v2: 8 pages (10pt), a false statement in the proof of Fact 2.4 is replaced with a true one; v1: 8 pages

References in corpus (1)

• Finitely generated infinite simple groups of infinite commutator width

Cited by in corpus (4)

• Groups of finite Morley rank with solvable local subgroups
• Stability and Bounded Balls of Free Products
• Embeddings and chains of free groups
• Model theoretic connected components of groups