Embedding free Burnside groups in finitely presented groups

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We construct an embedding of a free Burnside group B(m,n) of odd exponent n > 248 and rank m >1 in a finitely presented group with some special properties. The main application of this embedding is an easy construction of finitely presented nonamenable groups without noncyclic free subgroups (which provides a new finitely presented counterexample to the von Neumann problem on amenable groups). As another application, we construct weakly finitely presented groups of odd exponent n ≫ 1 which are not locally finite.

Original languageEnglish (US)
Pages (from-to)87-105
Number of pages19
JournalGeometriae Dedicata
Issue number1
StatePublished - Mar 2005


  • Amenable groups
  • Finitely presented groups
  • Free Burnside groups

ASJC Scopus subject areas

  • Geometry and Topology


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