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

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Book cover Geometry and Dynamics of Groups and Spaces

Part of the book series: Progress in Mathematics ((PM,volume 265))

Abstract

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.

Partially supported by NSF grants DMS-0600975 and DMS-0456185.

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Author information

Authors and Affiliations

  1. Département de mathématiques, Université de Strasbourg, 7 rue Descartes, F-67084, Strasbourg

    Thomas Delzant

  2. Department of Mathematics, Texas A & M University, MS-3368, College Station, TX, 77843-3368, USA

    Rostislav Grigorchuk

Authors
  1. Thomas Delzant
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  2. Rostislav Grigorchuk
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Yale University, 10 Hillhouse Avenue, New Haven, CT, 06520, USA

    Mikhail Kapranov

  2. Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111, Bonn, Germany

    Yuri Ivanovich Manin  & Pieter Moree  & 

  3. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs’ka, 3, 01601, Kyiv, Ukraine

    Sergiy Kolyada

  4. UFR de Mathématiques, Université de Lille 1, 59655, Villeneuve d’Ascq Cedex, France

    Leonid Potyagailo

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Dedicated to the memory of Sasha Reznikov

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Delzant, T., Grigorchuk, R. (2007). Homomorphic Images of Branch Groups, and Serre’s Property (FA). In: Kapranov, M., Manin, Y.I., Moree, P., Kolyada, S., Potyagailo, L. (eds) Geometry and Dynamics of Groups and Spaces. Progress in Mathematics, vol 265. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8608-5_7

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