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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The length and thickness of words
in a free group


Author: R. Z. Goldstein
Journal: Proc. Amer. Math. Soc. 127 (1999), 2857-2863
MSC (1991): Primary 20E05
Published electronically: May 4, 1999
MathSciNet review: 1641693
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we generalize the notion of a cut point of a graph. We assign to each graph a non-negative integer, called its thickness, so that a graph has thickness 0 if and only if it has a cut point. We then apply a method of J. H. C. Whitehead to show that if the coinitial graph of a given word has thickness $t$, then any word equivalent to it in a free group of rank $n$ has length at least $2nt$. We also define what it means for a word in a free group to be separable and we show that there is an algorithm to decide whether or not a given word is separable.


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Additional Information

R. Z. Goldstein
Affiliation: Department of Mathematics, State University at Albany, 1400 Washington Ave., Albany, New York 12222

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05142-4
PII: S 0002-9939(99)05142-4
Received by editor(s): January 11, 1998
Published electronically: May 4, 1999
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1999 American Mathematical Society