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