Yves Cornulier, Aditi Kar
August 13, 2010
We characterize permutational wreath products with Property (FA). For instance, we show that the standard wreath product A ≀ B of two non-trivial countable groups A and B has Property (FA) if and only if B has Property (FA) and A is a finitely generated group with finite abelianization. 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.