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On non-Archimedean lengths in groups

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  26 February 2010

David L. Wilkens
David L. Wilkens
Affiliation:
Department of Pure Mathematics, The University, Birmingham B15 2TT.
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Extract

A length function, for a group, associates to an element x a real number |x| subject to certain axioms, including a cancellation axiom which embodies certain cancellation properties for elements of a free group. Integer valued length functions were introduced by Roger Lyndon [1] where, with a more restrictive set of axioms than ours, it is shown that a length function for a group is given by a restriction of the usual length function on some free product.

MSC classification

Secondary: 20F99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 23 , Issue 1 , June 1976 , pp. 57 - 61
Copyright
Copyright © University College London 1976

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References

1.Lyndon, Roger C.. “Length functions in groups”, Math. Scand., 12 (1963), 209–234.CrossRefGoogle Scholar
2.Harrison, Nancy. “Real length functions in groups”, Trans. Atner. Math. Soc., 174 (1972), 77–106.CrossRefGoogle Scholar