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On length functions and normal forms in groups

Published online by Cambridge University Press:  24 October 2008

Bernard Hurley
Bernard Hurley
Affiliation:
Department of Mathematics, The City University, St John's Street, London EC1 V 4PB
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Extract

1. Introduction. Abstract length functions were first considered axiomatically in Lyndon (4). Length functions satisfying a less restrictive set of axioms were studied by Chiswell(1). Groups with a normal form structure (NFS-groups) were studied in Hurley (3) using a slightly different axiomatization to that used in this paper. Length functions naturally arise from normal form structures. In this paper we show that the length functions arising from normal form structures can be characterized axiomatic-ally by a set of axioms that consists of those of (1) together with one further axiom.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 3 , November 1978 , pp. 455 - 464
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1)Chiswell, I. M.Abstract length functions in groups. Math. Proc. Cambridge Philos. Soc. 86 (1976), 451–463.CrossRefGoogle Scholar
(2)Hoare, A. H. M.On length functions and Nielson methods in free groups. J. London Math. Soc. 14 (1) (1976), 188–192.CrossRefGoogle Scholar
(3)Hurley, B. M. Embedding theorems for groups, M.Sc. dissertation (Oxford, 1972).Google Scholar
(4)Lyndon, R. C.Length functions in groups. Math. Scand. 12 (1963), 209–234.CrossRefGoogle Scholar