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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 3 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.1007/s13373-013-0031-5
  • Title of Journal : BULLETIN OF MATHEMATICAL SCIENCES
  • Page Numbers: pp.73-131

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.