Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T11:35:06.776Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonsingular systems of two length three equations over a group

Published online by Cambridge University Press:  24 October 2008

James Howie
James Howie
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper we consider the conjecture of Kervaire, that a nonsingular system of equations in one or more variables over an arbitrary group G has a solution in some overgroup of G.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 1 , July 1991 , pp. 11 - 24
Copyright
Copyright © Cambridge Philosophical Society 1991

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

REFERENCES

[1]Bogley, W. and Pride, S. J.. Aspherical relative presentations. Proc. Edinburgh Math. Soc. (to appear).Google Scholar
[2]Edjvet, M.. The solution to certain sets of equations over groups. In Groups-St. Andrews, 1989 (eds Campbell, C. M. and Robinson, E. F.), vol. 1, London Math. Soc. Lecture Notes Series no. 159 (Cambridge University Press, 1991), pp. 105–123.CrossRefGoogle Scholar
[3]Edjvet, M.. Equations over groups and a theorem of Higman, Neumann and Neumann. Proc. London Math. Soc. (to appear).Google Scholar
[4]Edjvet, M. and Howie, J.. The solution of length four equations over groups. Trans. Amer. Math. Soc. (to appear).Google Scholar
[5]Gersten, S. M.. Nonsingular equations of small weight over groups. In Combinatorial Group Theory and Topology (eds Gersten, S. M. and Stallings, J. R.), Annals of Mathematics Studies vol. 111 (Princeton University Press, 1987), pp. 121–144.CrossRefGoogle Scholar
[6]Gersten, S. M.. Reducible diagrams and equations over groups. In Essays in Group Theory (ed. Gersten, S. M.), MSRI publications vol. 8 (Springer-Verlag, 1987), pp. 15–73.CrossRefGoogle Scholar
[7]Gersten, S. M.. On certain equations over torsion free groups (preprint).Google Scholar
[8]Gerstenhaber, M. and Rothaus, O. S.. The solution of sets of equations in groups. Proc. Nat. Acad. Sci. USA 48 (1962), 1531–1533.CrossRefGoogle ScholarPubMed
[9]Howie, J.. The solution of length three equations over groups. Proc. Edinburgh Math. Soc. 26 (1983), 89–96.CrossRefGoogle Scholar
[10]Howie, J.. On pairs of 2-complexes and systems of equations over groups. J. Reine Angew. Math. 324 (1981), 165–174.Google Scholar
[11]Levin, F.. Solutions of equations over groups. Bull. Amer. Math. Soc. 68 (1962), 603–604.CrossRefGoogle Scholar
[12]Pride, S. J.. Star-complexes and the dependence problem for hyperbolic complexes. Glasgow Math. J. 30 (1988), 155–170.CrossRefGoogle Scholar
[13]Rothaus, O. S.. On the nontriviality of some group extensions given by generators and relations. Ann. of Math. (2) 106 (1977), 559–612.CrossRefGoogle Scholar
[14]Siederadski, A. J.. A colouring test for asphericity. Quart. J. Math. Oxford Ser. (2) 34 (1983), 97–106.CrossRefGoogle Scholar