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On words of minimal length under endomorphisms of a free group

Published online by Cambridge University Press:  24 October 2008

Charles C. Edmunds
Charles C. Edmunds
Affiliation:
Mount Saint Vincent University, Halifax, Nova Scotia
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Extract

In (1) it is remarked that theorem 5·10 is an analogue, for endomorphisms of a free group, of a result of A. Shenitzer ((3), theorem 2) about automorphisms. With this in mind, D. Solitar asked the author if there might also be an analogue for the corollary on page 276 of(3). There is such an analogue and, after a preliminary discussion of definitions and notation, we will describe it.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 2 , March 1978 , pp. 191 - 194
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1)Edmunds, C. C.On the endomorphism problem for free groups: II. Proc. London Math. Soc. (to appear).Google Scholar
(2)Higgins, P. J. and Lyndon, R. C.Equivalence of elements under automorphisms of a free group. J. London Math. Soc. 8 (1974), 254–258.CrossRefGoogle Scholar
(3)Shenitzeb, A.Decomposition of a group with a single defining relator into a free product. Proc. Amer. Math. Soc. 6 (1955), 273–279.CrossRefGoogle Scholar
(4)Whitehead, J. H. C.On certain sets of elements in a free group. Proc. London Math. Soc. 41 (1936), 48–56.CrossRefGoogle Scholar