CYCLIC SUBGROUPS ARE QUASI-ISOMETRICALLY EMBEDDED IN THE THOMPSON--STEIN GROUPS

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Author: Claire Wladis
Date: February-March 2011
Publisher: World Scientific Publishing Co. Pte Ltd.
Document Type: Article
Length: 117 words

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Abstract :

To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1142/S0218196711006212 Byline: CLAIRE WLADIS We give criteria for determining the approximate length of elements in any given cyclic subgroup of the Thompson--Stein groups F(n.sub.1,...,n.sub.k) such that n.sub.1 - 1|n.sub.i - 1 ai [is an element oi] {1,...,k} in terms of the number of leaves in the minimal tree-pair diagram representative. This leads directly to the result that cyclic subgroups are quasi-isometrically embedded in the Thompson--Stein groups. This result also leads to the corollaries that Z.sup.n is also quasi-isometrically embedded in the Thompson--Stein groups for all n [is an element oi] a and that the Thompson--Stein groups have infinite dimensional asymptotic cone.

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Gale Document Number: GALE|A464502021