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Equations with torsion-free coefficients

Published online by Cambridge University Press:  20 January 2009

Andrew Clifford  and
Richard Z. Goldstein
Andrew Clifford
Affiliation:
Department of Mathematics and Statistics, The College of New Jersey, PO Box 7718, Ewing, NJ 08628-0718, USA
Richard Z. Goldstein
Affiliation:
Department of Mathematics and Statistics, State University of New York at Albany, Albany, NY 12222, USA
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Abstract

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In this paper we generalize techniques used by Klyachko and the authors to prove some tessellation results about S2. These results are applied to prove the solvability of certain equations with torsion-free coefficients.

Keywords

equations over groupsrelative pictures
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 2 , June 2000 , pp. 295 - 307
Copyright
Copyright © Edinburgh Mathematical Society 2000

References

1. Bogley, W. A. and Pride, S. J., Aspherical relative presentations, Proc. Edinb. Math. Soc. 35 (1992), 1–39.CrossRefGoogle Scholar
2. Brodskii, S. D. and Howie, J., One relator products of torsion-free groups, Glasgow Math. J. 35 (1993), 99–104.CrossRefGoogle Scholar
3. Clifford, A. and Goldstein, R. Z., Tesselations of S2 and equations over torsion-free groups, Proc. Edinb. Math. Soc. 38 (1995), 485–493.CrossRefGoogle Scholar
4. Edjvet, M., Equations over groups and a theorem of Higman, Neumann, and Neumann, Proc. Land. Math. Soc. 62 (1991), 563–589.CrossRefGoogle Scholar
5. Edjvet, M. and Juhasz, A., On equations over groups, Int. J. Alg. Comp. 4 (1994), 451–468.CrossRefGoogle Scholar
6. Gersten, S. M., Reducible diagrams and equations over groups, in Essays in group theory (ed. Gersten, S. M.) (Mathematical Sciences Research Institute Publications, New York, 1987).CrossRefGoogle Scholar
7. Howie, J., The solution of length three equations over groups, Proc. Edinb. Math. Soc. 26 (1983), 89–96.CrossRefGoogle Scholar
8. Klyachko, A. A., A funny property of sphere and equations over groups, Commun. Alg. 21 (1993), 2555–2575.CrossRefGoogle Scholar
9. Levin, F., Solutions of equations over groups, Bull. Am. Math. Soc. 68 (1962), 603–604.CrossRefGoogle Scholar
10. Sieradski, A. J., A coloring test for asphericity, Q. J. Math. Oxford 34 (1983), 97–106.CrossRefGoogle Scholar
11. Stallings, J. R., A graph-theoretic lemma and group embeddings, in Combinatorial group theory and topology (ed. S. M. Gersten and J. R. Stallings), Annals of Mathematical Studies, vol. 111 (1987), pp. 145–155.Google Scholar