A quick test for nonisomorphism of one-relator groups

Horadam, K. J.

doi:10.1090/S0002-9939-1981-0593456-3

A quick test for nonisomorphism of one-relator groups
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by K. J. Horadam PDF

Proc. Amer. Math. Soc. 81 (1981), 195-200 Request permission

Abstract:

A sequence of integers is read off from the presentation of a finitely generated torsion-free one-relator group with nontrivial second integral homology, without recourse to group-theoretic manipulations. This test sequence is derived from the cup coproduct on the coring of the integral homology module of the group, and reflects information about the group’s second lower central factor group. Test sequences differ only if the corresponding groups are nonisomorphic. The test process can be generalised to any one-relator group with nontrivial second integral homology.

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