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An embedding for groups with length functions

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  26 February 2010

A. H. M. Hoare
A. H. M. Hoare
Affiliation:
University of Birmingham, Department of Pure Mathematics, Birmingham, B15 2TT.
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Extract

Lyndon's axiomatic methods are used in [1] to show, among other things, that a group G with an integer valued length function satisfying certain conditions is free. At the end of his paper [2] Lyndon gives a method of embedding such a group in a free group whose natural length function extends the function on G. We construct here a simpler embedding with the same property.

MSC classification

Secondary: 20F99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 26 , Issue 1 , June 1979 , pp. 99 - 102
Copyright
Copyright © University College London 1979

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References

1.Hoare, A. H. M.. “On length functions and Nielson methods in free groups” J. London Math. Soc.,(2) 14, (1976), 188–192.CrossRefGoogle Scholar
2.Lyndon, R. C.. “Length functions in groups” Math. Scand., 12 (1963) 209–234.CrossRefGoogle Scholar