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Subgroups of finite index in groups with finite complete rewriting systems

Published online by Cambridge University Press:  20 January 2009

S. J. Pride  and
Jing Wang
S. J. Pride
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK
Jing Wang
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK
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Abstract

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We show that if a group G has a finite complete rewriting system, and if H is a subgroup of G with |G : H| = n, then H * Fn–1 also has a finite complete rewriting system (where Fn–1 is the free group of rank n – 1).

Keywords

complete rewriting systemdirected 2-complexsubgroup
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 1 , February 2000 , pp. 177 - 183
Copyright
Copyright © Edinburgh Mathematical Society 2000

References

1.Cohen, D. E., String rewriting – a survey for group theorists, in Geometric groups theory (ed. Niblo, G. A. and Roller, M. A.), vol. 1, pp. 37–47, London Mathematical Society Lecture Notes Series, no. 181 (Cambridge University Press, 1993).CrossRefGoogle Scholar
2.Comerford, L. P. Jr, Subgroups of small cancellation groups, J. Lond. Math. Soc. 17 (1978), 422–424.CrossRefGoogle Scholar
3.Fennessey, E. J. and Pride, S. J., Equivalences of two-complexes, with applications to NEC-groups, Math. Proc. Camb. Phil. Soc. 106 (1989), 215–228.CrossRefGoogle Scholar
4.Groves, J. R. J. and Smith, G. C., Rewriting systems and soluble groups, Bath Computer Science Technical Reports 89–19.Google Scholar
5.Groves, J. R. J. and Smith, G. C., Soluble groups with a finite rewriting system, Proc. Edinb. Math. Soc. 36 (1993), 283–288.CrossRefGoogle Scholar
6.Higgins, P. J., Notes on categories and groupoids (Van Nostrand Reinhold Company, London, 1971).Google Scholar
7.Otto, F., On properties of monoids that are modular for free products and for certain free products with amalgamated submonoids, Preprint, 1997.Google Scholar
8.Pride, S. J., Geometric methods in combinatorial semigroup theory, in Semigroups, formal languages and groups (ed. Fountain, J.), pp. 215–232 (Kluwer, Dordrecht, 1995).CrossRefGoogle Scholar
9.Pride, S. J., Star-complexes, and the dependence problems for hyperbolic complexes, Glasgow Math. J. 30 (1988), 155–170.CrossRefGoogle Scholar
10.Pride, S. J. and Wang, Jing, Rewriting systems, finiteness conditions, and associated functions, in Proc. Int. Conf, on Algorithmic Problems in Groups and Semigroups, Lincoln, NB, USA, 1998.Google Scholar