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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
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(5)Stallings, J. R.Group theory and three-dimensional manifolds (New Haven and London; Yale University Press, 1971).Google Scholar