Amenable groups without finitely presented amenable covers

Bulletin of Mathematical Sciences - Tập 3 - Trang 73-131 - 2013
Mustafa Gökhan Benli1, Rostislav Grigorchuk1, Pierre de la Harpe2
1Department of Mathematics, Texas A&M University, College Station, USA
2Section de Mathématiques, Université de Genève, Genève 4, Switzerland

Tóm tắt

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.

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