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Coherence for elementary amenable groups

Published:2024-01-11 Issue: Volume: Page:
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Hughes Sam,Kielak Dawid,Kropholler Peter,Leary Ian

Abstract

We prove that for an elementary amenable group, coherence of the group, homological coherence of the group, and coherence of the integral group ring are all equivalent. This generalises a result of Bieri and Strebel for finitely generated soluble groups.

Funder

Clay Mathematics Institute

Publisher

American Mathematical Society (AMS)

Link

https://www.ams.org/proc/0000-000-00/S0002-9939-2024-16656-9/proc16656_AM.pdf

Reference14 articles.

1. Morse theory and finiteness properties of groups;Bestvina, Mladen;Invent. Math.,1997

2. A geometric invariant of discrete groups;Bieri, Robert;Invent. Math.,1987

3. Trees, valuations, and the Bieri-Neumann-Strebel invariant;Brown, Kenneth S.;Invent. Math.,1987

4. Almost finitely presented soluble groups;Bieri, Robert;Comment. Math. Helv.,1978

5. Soluble groups with coherent group rings;Bieri, Robert,1979

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