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Abstract length functions in groups

Published online by Cambridge University Press:  24 October 2008

I. M. Chiswell
I. M. Chiswell
Affiliation:
Queen Mary College, University of London
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Extract

If F is a free group on some fixed basis X, there is a mapping from F to the non-negative integers, given by sending an element of F to the length of the normal word in X±1 representing it. A similar mapping is obtained in the case of a free product of groups. Lyndon (3) considered mappings from an arbitrary group to the non-negative integers having certain properties in common with these mappings on free groups and free products.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 3 , November 1976 , pp. 451 - 463
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

REFERENCES

(1)Harrison, N.Real length functions in groups. Trans. Amer. Math. Soc. 174 (1972), 77–106.CrossRefGoogle Scholar
(2)Karrass, A. and Solitar, D.The subgroups of a free product of two groups with an amalgamated subgroup. Trans. Amer. Math. Soc. 149 (1970), 227–255.CrossRefGoogle Scholar
(3)Lyndon, R. C.Length functions in groups. Math. Scand. 12 (1963), 209–234.CrossRefGoogle Scholar
(4)Serre, J.-P.Arbres, amalgames et SL2. To appear as Springer Lecture Notes.Google Scholar
(5)Stallings, J. R.Group theory and three-dimensional manifolds (New Haven and London; Yale University Press, 1971).Google Scholar