Homomorphic images of branch groups and Serre's FA property

Thomas Delzant (1) , Rostislav Grigorchuk (1)

1 IRMA - Institut de Recherche Mathématique Avancée

It is shown that a finitely generated branch group has Serre's (FA) property if and only if it does not surjects onto an infinite cyclic or infinite dihedral goup. Example of finitely generated self-similar branch groups surjecting onto an infinite cyclic or infinite dihedral group are constructed.

Mots clés: branch groups

Domaines: Géométrie différentielle [math.DG]

Thomas Delzant, Rostislav Grigorchuk. Homomorphic images of branch groups and Serre's FA property. 2007. ⟨hal-00140726⟩