Amenable groups without finitely presented amenable covers

Mustafa Gokhan Benli; Rostislav Grigorchuk; Pierre De La Harpe

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arXiv · 1206.2072

Amenable groups without finitely presented amenable covers

Mustafa Gokhan Benli·Rostislav Grigorchuk·Pierre De La Harpe

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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 $E$ 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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BibTeX RIS

Mustafa Gokhan Benli, Rostislav Grigorchuk, Pierre De La Harpe. 2013-05-03. Amenable groups without finitely presented amenable covers. https://arxiv.org/abs/1206.2072

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