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Soluble groups with a finite rewriting system

Published online by Cambridge University Press:  20 January 2009

J. R. J. Groves  and
G. C. Smith
J. R. J. Groves
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Australia 3052
G. C. Smith
Affiliation:
School of Mathematical Sciences, University of Bath, England
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Abstract

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We describe a class of soluble groups with a finite complete rewriting system which includes all the soluble groups known to have such a system. It is an open question, related to deep questions in the theory of groups, whether it includes all soluble groups with such a system.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , Issue 2 , June 1993 , pp. 283 - 288
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

REFERENCES

1.Åberg, Hans, Bieri-Strebel valuations (of finite rank), Proc. London Math. Soc. (3) 52 (1986), 269–304.CrossRefGoogle Scholar
2.Anick, D. J., On the homology of associative algebras, Trans. Amer. Math. Soc. 296 (1986), 641–659.CrossRefGoogle Scholar
3.Baumslag, G. and Bieri, R., Constructable solvable groups, Math. Z. 151 (1976), 249–257.CrossRefGoogle Scholar
4.Brown, K. S., The geometry of rewriting systems: A proof of the Anick–Groves–Squier Theorem, Proceedings of the Workshop on Algorithms, Word Problems and Classification Combinatorial Group Theory (MSRI Publications, Springer-Verlag, 1991).Google Scholar
5.Groves, J. R. J., Rewriting systems and homology of groups, in Groups–Canberra 1989 (ed. Kovacs, L. G., Lecture Notes in Mathematics 1456, Springer-Verlag, Berlin, Heidelberg, New York, 1990), 114–141.CrossRefGoogle Scholar
6.Groves, J. R. J. and Smith, G. C., Rewriting systems and soluble groups, preprint.Google Scholar
7.Jantzen, M., Confluent String Rewriting (EACTS monographs on Theoretical Computer Science, Springer-Verlag, Berlin, 1988).CrossRefGoogle Scholar
8.Kropholler, P. H., Cohomological dimension of solvable groups, J. Pure Appl. Algebra 43 (1986), 281–287.CrossRefGoogle Scholar
9.Le Chenadec, Ph., Canonical forms in finitely presented algebras (Pitman, London; John Wiley & Sons, New York, 1986).Google Scholar
10.Sims, G. C., Verifying nilpotence, J. Symbolic Computation 3 (1987), 231–248.CrossRefGoogle Scholar
11.Squier, Craig C., Word problems and a homological finiteness condition for modules, J. Pure Appl. Algebra 49 (1987), 201–217.CrossRefGoogle Scholar