Homomorphic Images of Branch Groups, and Serre’s Property (FA)

  • Thomas Delzant
  • Rostislav Grigorchuk
Part of the Progress in Mathematics book series (PM, volume 265)


It is shown that a finitely generated branch group has Serre’s property (FA) if and only if it does not surject onto the infinite cyclic group or the infinite dihedral group. An example of a finitely generated self-similar branch group surjecting onto the infinite cyclic group is constructed.


Property (FA) branch group tree hyperbolic space indicable group 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Thomas Delzant
    • 1
  • Rostislav Grigorchuk
    • 2
  1. 1.Département de mathématiquesUniversité de StrasbourgStrasbourg
  2. 2.Department of MathematicsTexas A & M UniversityCollege StationUSA

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