Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-20T10:56:14.507Z Has data issue: false hasContentIssue false
  • English
  • Français

On the asphericity of one-relator relative presentations

Published online by Cambridge University Press:  14 November 2011

Martin Edjvet
Martin Edjvet
Affiliation:
Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the 1-relator relative presentation 〈H, x|xaxbx−1c〉 where H is a group, a, b, c ∈ H, x ∉ H and b, c ≠ 1. We give necessary and sufficient conditions for this presentation to be aspherical apart from two outstanding special cases which remain open.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 4 , 1994 , pp. 713 - 728
Copyright
Copyright © Royal Society of Edinburgh 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Bogley, W. A. and Pride, S. J.. Aspherical relative presentations. Proc. Edinburgh Math. Soc. 35 (1992), 1–39.CrossRefGoogle Scholar
2Collins, D. J. and Huebschmann, J.. Spherical diagrams and identities among relations. Math. Ann. 261 (1982), 155–183.Google Scholar
3Edjvet, M.. Equations over groups and a theorem of Higman, Neumann and Neumann. Proc. London Math. Soc. (3) 62 (1991), 563–589.Google Scholar
4Howie, J.. The solution of length three equations over groups. Proc. Edinburgh Math. Soc. 26 (1983), 89–96.Google Scholar
5Huebschmann, J.. Cohomology theory of aspherical groups and of small cancellation groups. J. Pure Appl. Algebra 14(1979), 137–143.CrossRefGoogle Scholar
6Pride, S. J.. Identities among relations of group presentations. In Group Theory from a Geometrical Viewpoint, eds. Ghys, E., Haefliger, A. and Verjovsky, A., 687–717 (Singapore: World Scientific, 1991).Google Scholar