The length and thickness of words in a free group
Author:
R. Z. Goldstein
Journal:
Proc. Amer. Math. Soc. 127 (1999), 28572863
MSC (1991):
Primary 20E05
Published electronically:
May 4, 1999
MathSciNet review:
1641693
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Abstract: In this paper we generalize the notion of a cut point of a graph. We assign to each graph a nonnegative 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 , then any word equivalent to it in a free group of rank has length at least . 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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 R. Goldstein and E. C. Turner, Automorphisms of Free Groups and Their Fixed Points, Invent. Math. 78 (1984), 112. MR 86h:20031
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 A. Shenitzer, Decomposition of a Group with a Single Defining Relation into a Free Product, Proc. Amer. Math. Soc. 6 (1955), 273279. MR 16:995c
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 J. Singer, Three Dimensional Manifolds and Their Heegaard Diagrams, Trans Amer. Math. Soc. 35 (1933), 88111.
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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/S0002993999051424
PII:
S 00029939(99)051424
Received by editor(s):
January 11, 1998
Published electronically:
May 4, 1999
Communicated by:
Ronald M. Solomon
Article copyright:
© Copyright 1999
American Mathematical Society
