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Endomorphisms of free groups and their fixed points

Published online by Cambridge University Press:  04 October 2011

W. Imrich  and
E. C. Turner
W. Imrich
Affiliation:
Institut für Mathematik und Angewandte Geometrie, Montanuniversität Leoben, A-8700 Leoben, Austria
E. C. Turner
Affiliation:
Department of Mathematics and Statistics, State University of New York at Albany, Albany, NY 12222, U.S.A.
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Extract

Much work recently has been focused on the issue of fixed words for automorphisms of free groups - see [2] and papers referred to there. Bestvina and Handel [1] have announced a powerful structure theorem for automorphisms of free groups that has as a consequence a proof of what has become known, to the amusement of Peter Scott, as the ‘so-called’ Scott Conjecture: if F is a free group of rank n and α:F→F is an automorphism, then Fix (α) = {w∈F|α(w) = w} has rank at most n.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 3 , May 1989 , pp. 421 - 422
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

[1] Bestvina, M.. Lecture at Cornell Topology Festival, (May 1988).Google Scholar
[2] Goldstein, R. Z. and Turner, E. C.. Fixed subgroups of homomorphisms of free groups. Bull. London Math. Soc. 18 (1986), 468–470.CrossRefGoogle Scholar
[3] Imrich, W. and Turner, E. C.. Fixed subsets of homomorphisms of free groups. (Unpublished manuscript.)Google Scholar
[4] Lyndon, R. C. and Schupp, P. E.. Combinatorial Group Theory (Springer-Verlag, 1977).Google Scholar
[5] Magnus, W., Karass, A. and Solitar, D.. Combinatorial Group Theory (Wiley, 1966).Google Scholar