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Equivalences of two-complexes, with applications to NEC-groups

Published online by Cambridge University Press:  28 June 2011

Eric J. Fennessey  and
Stephen J. Pride
Eric J. Fennessey
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
Stephen J. Pride
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
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Abstract

In [17] the second author introduced the concept of an involutary presentation. Such presentations are useful when one wants to deal geometrically with groups which have generators of order two. Now if one wants to deal with subgroups of such groups then it is no longer adequate to stick to presentations - one must consider arbitrary 2-complexes. However, these 2-complexes will differ from those which are usually considered, in that we need to allow some edges to be equal to their inverses.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 2 , September 1989 , pp. 215 - 228
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

[1] Bujalance, E.. Normal subgroups of NEC groups, Math. Z. 178 (1981), 331–341.CrossRefGoogle Scholar
[2] Bujalance, J. A.. Normal subgroups of even index in an NEC group, Arch. Math. (Basel) 49 (1987), 470–478.CrossRefGoogle Scholar
[3] Edjvet, M and Howie, J.. Star graphs, projective planes and free subgroups in small cancellation groups. Proc. London Math. Soc. (3), 57 (1988), 301–328.CrossRefGoogle Scholar
[4] El-Mosalamy, M. S.. Free subgroups of small cancellation groups. Israel J. Math. 56 (1986), 345–348.CrossRefGoogle Scholar
[5] El-Mosalamy, M. S.. Applications of star-complexes in group theory. Ph.D. thesis, University of Glasgow (1987).Google Scholar
[6] Gersten, S. M.. Reducible diagrams and equations over groups. In Essays in Group Theory (Springer-Verlag, 1987), pp. 15–73.CrossRefGoogle Scholar
[7] Hill, P., Pride, S. J. and Vella, A. D.. On the T(q)-conditions of small cancellation theory, Israel J. Math. 52 (1985), 293–304.CrossRefGoogle Scholar
[8] Hoare, A. H. M.. Subgroups of NEC groups and finite permutation groups. (Preprint, 1988).Google Scholar
[9] Hoare, A. H. M., Karrass, A. and Solitar, D.. Subgroups of finite index in Fuchsian groups. Math Z. 120 (1971), 289–298.CrossRefGoogle Scholar
[10] Hoare, A. H. M., Karrass, A. and Solitar, D.. Subgroups of infinite index in Fuchsian groups. Math. Z. 125 (1972), 59–69.CrossRefGoogle Scholar
[11] Hoare, A. H. M., Karrass, A. and Solitar, D.. Subgroups of NEC groups. Comm. Pure Appl. Math. 26 (1973), 731–744.CrossRefGoogle Scholar
[12] Lyndon, R. C. and Schupp, P. E.. Combinatorial Group Theory (Springer-Verlag, 1977).Google Scholar
[13] MacBeath, A. M. and Hoare, A. H. M.. Groups of hyperbolic crystallography. Math. Proc. Cambridge Philos. Soc. 79 (1976), 235–249.CrossRefGoogle Scholar
[14] Magnus, W., Karrass, A. and Solitar, D.. Combinatorial Group Theory (Dover, 1976).Google Scholar
[15] Napthine, A. K. and Pride, S. J.. On generalized braid groups. Glasgow Math. J. 28 (1986), 199–209.CrossRefGoogle Scholar
[16] Pride, S. J.. Star-complexes, and the dependence problems for hyperbolic complexes. Glasgow Math. J. 30 (1988), 155–170.CrossRefGoogle Scholar
[17] Pride, S. J.. Involuntary presentations, with applications to Coxeter groups, NEC groups and groups of Kanevskiῐ. J. Algebra 120 (1989), 200–223.CrossRefGoogle Scholar