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Homological dimension of elementary amenable groups

Homological dimension of elementary amenable groups
Homological dimension of elementary amenable groups
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.
0075-4102
Kropholler, Peter
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Martinez-Perez, Conchita
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Kropholler, Peter
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Martinez-Perez, Conchita
32bbe45a-bcda-4610-a52a-3ba2312a1691

Kropholler, Peter and Martinez-Perez, Conchita (2019) Homological dimension of elementary amenable groups. Journal für die reine und angewandte Mathematik. (doi:10.1515/crelle-2019-0008). (In Press)

Record type: Article

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.

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KMP-resubmission 24 Feb 2019 - Accepted Manuscript
Restricted to Repository staff only until 23 February 2020.
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Accepted/In Press date: 23 February 2019

Identifiers

Local EPrints ID: 428835
URI: https://eprints.soton.ac.uk/id/eprint/428835
ISSN: 0075-4102
PURE UUID: 06f426b0-d27d-4598-824d-e9730de51035

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Date deposited: 11 Mar 2019 17:30
Last modified: 01 Apr 2019 16:30

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Author: Conchita Martinez-Perez

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