On Property (FA) for wreath products

Abstract

We characterize permutational wreath products with Property (FA). For instance, the standard wreath product A wr B of two nontrivial countable groups A,B, has Property (FA) if and only if B has Property (FA) and A is a finitely generated group with finite abelianisation. We also prove an analogous result for hereditary Property (FA). On the other hand, we prove that many wreath products with hereditary Property (FA) are not quotients of finitely presented groups with the same property.

12 pages, 0 figure

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Cited by in corpus (6)

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• New examples of groups acting on real trees
• An (FA)-group that is not (FR)
• Property FW and wreath products of groups: a simple approach using Schreier graphs
• Some H1F-groups with unbounded torsion and a conjecture of Kropholler and Mislin
• Wreath products of groups acting with bounded orbits