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Torsion-free soluble groups, completions, and the zero divisor conjecture

Torsion-free soluble groups, completions, and the zero divisor conjecture
Torsion-free soluble groups, completions, and the zero divisor conjecture
This paper contains two results which bear upon the zero-divisor conjecture for group rings. The first, proved using commutative algebra, asserts that a finitely generated torsion-free meta- belian-by-finite group has many torsion-free quotients of finite rank. The second result concerns the completion of the group algebra kG at its augmentation ideal when G is a polycyclic pro-p group and k is an algebraically closed field of characteristics p>0. For example, if G is torsion-free it is shown that this completion is a domain. These two results imply that if G is a torsion-free soluble group of derived length at most three, and K is a field of characteristics zero, then KG is a domain.
181-196
Crawley-Boevey, W.W.
c800360a-b40d-4565-9b39-d86fdca34cd2
Kropholler, P.H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Linnell, P.A.
6fc87ccd-1915-4008-bba6-1cfced0af540
Crawley-Boevey, W.W.
c800360a-b40d-4565-9b39-d86fdca34cd2
Kropholler, P.H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Linnell, P.A.
6fc87ccd-1915-4008-bba6-1cfced0af540

Crawley-Boevey, W.W., Kropholler, P.H. and Linnell, P.A. (1988) Torsion-free soluble groups, completions, and the zero divisor conjecture. Journal of Pure and Applied Algebra, 54 (2-3), 181-196. (doi:10.1016/0022-4049(88)90029-1).

Record type: Article

Abstract

This paper contains two results which bear upon the zero-divisor conjecture for group rings. The first, proved using commutative algebra, asserts that a finitely generated torsion-free meta- belian-by-finite group has many torsion-free quotients of finite rank. The second result concerns the completion of the group algebra kG at its augmentation ideal when G is a polycyclic pro-p group and k is an algebraically closed field of characteristics p>0. For example, if G is torsion-free it is shown that this completion is a domain. These two results imply that if G is a torsion-free soluble group of derived length at most three, and K is a field of characteristics zero, then KG is a domain.

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Published date: October 1988
Organisations: Mathematical Sciences

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Local EPrints ID: 349627
URI: https://eprints.soton.ac.uk/id/eprint/349627
PURE UUID: dd4b041a-34fd-48ff-95cb-d767031828fc

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Date deposited: 12 Mar 2013 12:43
Last modified: 18 Jul 2017 04:39

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