Homological dimension of elementary amenable groups-Reference-Cited by-同舟云学术

Homological dimension of elementary amenable groups

Published:2019-06-14 Issue:766 Volume:2020 Page:45-60
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Kropholler Peter H.¹^ORCID,Martínez-Pérez Conchita²^ORCID

Affiliation:

1. Mathematical Sciences , University of Southampton , Southampton , United Kingdom

2. University of Zaragoza , Zaragoza , Spain

Abstract

Abstract In this paper we prove that the homological dimension of an elementary amenable group over an arbitrary commutative coefficient ring is either infinite or equal to the Hirsch length of the group. Established theory gives simple group theoretical criteria for finiteness of homological dimension and so we can infer complete information about this invariant for elementary amenable groups. Stammbach proved the special case of solvable groups over coefficient fields of characteristic zero in an important paper dating from 1970.

Funder

Engineering and Physical Sciences Research Council

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2019-0008/pdf

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