Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

The length and thickness of words in a free group

Author(s): R. Z. Goldstein
Journal: Proc. Amer. Math. Soc. 127 (1999), 2857-2863.
MSC (1991): Primary 20E05
Posted: May 4, 1999
MathSciNet review: 1641693
Retrieve article in: PDF
This article is available free of charge

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 , 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.

References:

1.: R. Goldstein and E. C. Turner, Automorphisms of Free Groups and Their Fixed Points, Invent. Math. 78 (1984), 1-12. MR 86h:20031
2.: A. Shenitzer, Decomposition of a Group with a Single Defining Relation into a Free Product, Proc. Amer. Math. Soc. 6 (1955), 273-279. MR 16:995c
3.: J. Singer, Three Dimensional Manifolds and Their Heegaard Diagrams, Trans Amer. Math. Soc. 35 (1933), 88-111.
4.: J. H. C. Whitehead, On Certain Sets of Elements in a Free Group, Proc. London Math. Soc. 41 (1936), 48-56.
5.: J. H. C. Whitehead, On Equivalent Sets of Elements in a Free Group, Ann. of Math. 37 (1936), 782-800.

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|