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On a certain class of group presentations

Published online by Cambridge University Press:  24 October 2008

M. Edjvet
M. Edjvet
Affiliation:
Department of Mathematics, University of Nottingham, Nottingham NG7 2RD
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Extract

In [8] and [9] S. J. Pride has initiated a study of group presentations in which each defining relator involves exactly two members of the generating set. The methods there involve the use of graphs and so-called edge groups – the building blocks of such presentations. In this paper we replace ‘graph’ by ‘set of finite subsets of a given set’, and ‘edge group’ by ‘face group’ in order to study a larger class of presentations. This way we are able to extend to this larger class a Freiheitssatz and a result on diagrammatic asphericity which appear in the references cited above.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 1 , January 1989 , pp. 25 - 35
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

REFERENCES

[1]Appel, K. I. and Schupp, P. E., Artin groups and infinite Coxeter groups. Invent. Math. 72 (1983), 201–220.CrossRefGoogle Scholar
[2]Collins, D. and Huebschmann, J., Spherical diagrams and identities among relations. Math. Ann. 261 (1983), 155–183.CrossRefGoogle Scholar
[3]Edjvet, M.. Abstract simplicial complexes and group presentations. Brunel University TR12, 1986.Google Scholar
[4]Fine, B.. The Picard group and the modular group. In Proceedings Groups – St Andrews 1985. London Math. Soc. Lecture Note Series no. 121 (Cambridge University Press, 1986), pp. 150–163.Google Scholar
[5]Gurevich, G. A.. On the conjugacy problem for groups with one defining relator. Soviet Math. Dokl. 13 (1972), 1436–1439.Google Scholar
[6]Lyndon, R. C. and Schupp, P. E.. Combinatorial Group Theory (Springer-Verlag, 1977).Google Scholar
[7]Pride, S. J.. One-relator quotients of free products. Math. Proc. Cambridge Philos. Soc. 88 (1980), 233–243.CrossRefGoogle Scholar
[8]Pride, S. J.. Groups with presentations in which each defining relator involves exactly two generators. J. London Math. Soc. (2) 36 (1987), 245–256.CrossRefGoogle Scholar
[9]Pride, S. J.. The diagrammatic asphericity of groups given by presentations in which each defining relator involves exactly two types of generator. (Preprint, 1986.)Google Scholar