A quick test for nonisomorphism of one-relator groups

K. J. Horadam
1981 Proceedings of the American Mathematical Society  
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
more » ... rocess can be generalised to any one-relator group with nontrivial second integral homology.
doi:10.1090/s0002-9939-1981-0593456-3 fatcat:7xhvxynaujeadjewvxzcghlela