Amenable groups without finitely presented amenable covers

Benli M. G. , Grigorchuk R., de la Harpe P.

BULLETIN OF MATHEMATICAL SCIENCES, vol.3, no.1, pp.73-131, 2013 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 3 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.1007/s13373-013-0031-5
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.73-131
  • Keywords: Finitely generated groups, Finitely presented covers, Self-similar groups, Metabelian groups, Soluble groups, Groups of intermediate growth, Amenable groups, Groups with non-abelian free subgroups, Large groups, SOLUBLE GROUPS, GROWTH, AMENABILITY, TORSION, PRESENTATIONS, VALUATIONS, SUBGROUPS


The goal of this article is to study results and examples concerning finitely presented covers of finitely generated amenable groups. We collect examples of groups G with the following properties: (i) G is finitely generated, (ii) G is amenable, e.g. of intermediate growth, (iii) any finitely presented group with a quotient isomorphic to G contains non-abelian free subgroups, or the stronger (iii') any finitely presented group with a quotient isomorphic to G is large.