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Pregroups and length functions

Published online by Cambridge University Press:  24 October 2008

A. H. M. Hoare
A. H. M. Hoare
Affiliation:
Department of Mathematics, University of Birmingham
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Extract

Pregroups were defined by Stallings[7] who showed that the elements of the group they define have a normal form up to an equivalence called interleaving. Recently Rimlinger[5] has shown that subject to a discreteness and a boundedness condition any pregroup P defines a graph of groups. We show here that closer analysis of P makes the boundedness condition superfluous. In § 1 we give results of Stallings and Rimlinger and prove some key lemmas. In §2 we show that the discreteness condition gives an integer-valued length function in the sense of Lyndon [4]. It follows from the work of Chiswell [2] and Serre [6] that this defines a graph of groups. I would like to thank the referee for his careful reading and useful comments on this paper.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 1 , July 1988 , pp. 21 - 30
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

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