Catalog Home Page

A quick test for nonisomorphism of one-relator groups

Horadam, K.J. (1981) A quick test for nonisomorphism of one-relator groups. Proceedings of the American Mathematical Society, 81 (2). p. 195.

Link to Published Version: http://dx.doi.org/10.1090/S0002-9939-1981-0593456-...
*Subscription may be required

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.

Publication Type: Journal Article
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: American Mathematical Society
Copyright: © Copyright 1981 American Mathematical Society
URI: http://researchrepository.murdoch.edu.au/id/eprint/31271
Item Control Page Item Control Page