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Dimension of elementary amenable groups

Dimension of elementary amenable groups
Dimension of elementary amenable groups
This paper has three parts. It is conjectured that for every elementary amenable group G and every non-zero commutative ring k, the homological dimension hdk(G)is equal to the Hirsch length h(G) whenever G has no k-torsion. In Part I this conjecture is proved for several classes, including the abelian-by-polycyclic groups. In Part II it is shown that the elementary amenable groups of homological dimension one are colimits of systems of groups of cohomological dimension one. In Part III the deep problem of calculating the cohomological dimension of elementary amenable groups is tackled with particular emphasis on the nilpotent-by-polycyclic case, where a complete answer is obtained over Q for countable groups
0075-4102
1-27
Bridson, Martin R.
28b22b3b-2ff1-4b35-a3b7-cc2fd559e689
Kropholler, Peter H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Bridson, Martin R.
28b22b3b-2ff1-4b35-a3b7-cc2fd559e689
Kropholler, Peter H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4

Bridson, Martin R. and Kropholler, Peter H. (2013) Dimension of elementary amenable groups. Journal für die Reine Angewandte Mathematik, n/a, 1-27. (doi:10.1515/crelle-2013-0012).

Record type: Article

Abstract

This paper has three parts. It is conjectured that for every elementary amenable group G and every non-zero commutative ring k, the homological dimension hdk(G)is equal to the Hirsch length h(G) whenever G has no k-torsion. In Part I this conjecture is proved for several classes, including the abelian-by-polycyclic groups. In Part II it is shown that the elementary amenable groups of homological dimension one are colimits of systems of groups of cohomological dimension one. In Part III the deep problem of calculating the cohomological dimension of elementary amenable groups is tackled with particular emphasis on the nilpotent-by-polycyclic case, where a complete answer is obtained over Q for countable groups

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e-pub ahead of print date: 11 April 2013
Organisations: Mathematical Sciences

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Local EPrints ID: 350286
URI: https://eprints.soton.ac.uk/id/eprint/350286
ISSN: 0075-4102
PURE UUID: 7e65b385-c02e-4a88-897d-a77fb21db027

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Date deposited: 25 Mar 2013 11:33
Last modified: 18 Jul 2017 04:35

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