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 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 3 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.1007/s13373-013-0031-5
  • Journal Name: BULLETIN OF MATHEMATICAL SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-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
  • Middle East Technical University Affiliated: No

Abstract

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.