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Asphericity and zero divisors in group algebras

Asphericity and zero divisors in group algebras
Asphericity and zero divisors in group algebras
We use homology to prove the following result: suppose that X is a classifying space for a group H and that Y is obtained from X by attaching one 1-cell and one 2-cell. Suppose also that the kernel of the map from H to G (the fundamental group of Y) is acyclic and that the relative homology group H_1(Y,X) is finite. If Y is not a classifying space for G, then the integral group ring of G contains zero divisors. This is a generalization of a result proved recently in a different way by S. V. Ivanov.
0021-8693
362-364
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e

Leary, Ian J. (2000) Asphericity and zero divisors in group algebras. Journal of Algebra, 227 (1), 362-364. (doi:10.1006/jabr.1999.8238).

Record type: Article

Abstract

We use homology to prove the following result: suppose that X is a classifying space for a group H and that Y is obtained from X by attaching one 1-cell and one 2-cell. Suppose also that the kernel of the map from H to G (the fundamental group of Y) is acyclic and that the relative homology group H_1(Y,X) is finite. If Y is not a classifying space for G, then the integral group ring of G contains zero divisors. This is a generalization of a result proved recently in a different way by S. V. Ivanov.

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Published date: 2000

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Local EPrints ID: 29832
URI: http://eprints.soton.ac.uk/id/eprint/29832
DOI: doi:10.1006/jabr.1999.8238
ISSN: 0021-8693
PURE UUID: 3535eb66-f1cb-4b46-bc2e-fd5891db6f02
ORCID for Ian J. Leary: ORCID iD orcid.org/0000-0001-8300-4979

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Date deposited: 20 Jul 2006
Last modified: 16 Mar 2024 04:04

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Author: Ian J. Leary ORCID iD

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