The length and thickness of words in a free group
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- by R. Z. Goldstein PDF
- Proc. Amer. Math. Soc. 127 (1999), 2857-2863 Request permission
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.References
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Additional Information
- R. Z. Goldstein
- Affiliation: Department of Mathematics, State University at Albany, 1400 Washington Ave., Albany, New York 12222
- Received by editor(s): January 11, 1998
- Published electronically: May 4, 1999
- Communicated by: Ronald M. Solomon
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2857-2863
- MSC (1991): Primary 20E05
- DOI: https://doi.org/10.1090/S0002-9939-99-05142-4
- MathSciNet review: 1641693