Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T01:17:03.559Z Has data issue: false hasContentIssue false
  • English
  • Français

A certain non-singular system of length three equations over a group

Published online by Cambridge University Press:  20 January 2009

S. Wreth
S. Wreth
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH 14 4AS
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Kervaire Conjecture is correct if it can be shown to hold for non-singular systems of equations of length 3. In this paper we prove it for the case of equations over a group G where each equation has the form axbx−1cy = 1 for a, b, c ∈ G.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 3 , October 1997 , pp. 515 - 539
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

REFERENCES

1.Bogley, W. A. and Pride, S. J., Aspherical relative presentations, Proc. Edinburgh Math. Soc. 35 (1992), 1–39.CrossRefGoogle Scholar
2.Conder, M. D. E., Three-relator quotients of the modular group, Quart. J. Math. Oxford (2) 38 (1987), 427–447.CrossRefGoogle Scholar
3.Gersten, S. M., Reducible diagrams and equations over groups, in Essays in group theory (MSRI Publications 8, edited by Gersten, S. M., Springer-Verlag, 1987).CrossRefGoogle Scholar
4.Gerstenhaber, M. and Rothaus, O. S., The solution of equations in groups, Proc. Nat. Acad. Sci. USA 48 (1962), 1531–1533.CrossRefGoogle ScholarPubMed
5.Howie, J., On pairs of 2-complexes and systems of equations in groups, J Reine Angew. Math. 324 (1981), 165–174.Google Scholar
6.Howie, J., The solution of length three equations over groups, Proc. Edinburgh Math. Soc. 26 (1983), 89–96.CrossRefGoogle Scholar
7.Howie, J., Nonsingular systems of two length three equations over a group, Math. Proc. Cambridge Philos. Soc. (11), 110 (1991), 11–24.CrossRefGoogle Scholar
8.Metaftsis, V., Studies on one-relator products of groups (Ph.D. thesis, Heriot-Watt University, 1994).Google Scholar
9.Rothaus, O. S., On the non-triviality of some group extensions given by generators and relations, Ann. of Math. (2) 106 (1977), 559–612.CrossRefGoogle Scholar
10.Schönert, Martin et al. GAP – Groups, Algorithms, and Programming (Lehrstuhl D. für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, third edition, 1993).Google Scholar
11.Wreth, S., Hyperbolicity of one-relator products and equations over groups (Ph.D. thesis, Heriot-Watt University, 1995).Google Scholar