The word problem and the metric for the Thompson-Stein groups
| Autor: | Wladis, Claire |
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| Rok vydání: | 2008 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/jlms/jdq060 |
| Popis: | We consider the Thompson-Stein group F(n_1,...,n_k) for integers n_1,...,n_k and k greater than 1. We highlight several differences between the cases k=1$ and k>1, including the fact that minimal tree-pair diagram representatives of elements may not be unique when k>1. We establish how to find minimal tree-pair diagram representatives of elements of F(n_1,...,n_k), and we prove several theorems describing the equivalence of trees and tree-pair diagrams. We introduce a unique normal form for elements of F(n_1,...,n_k) (with respect to the standard infinite generating set developed by Melanie Stein) which provides a solution to the word problem, and we give sharp upper and lower bounds on the metric with respect to the standard finite generating set, showing that in the case k>1, the metric is not quasi-isometric to the number of leaves or caret in the minimal tree-pair diagram, as is the case when k=1. Comment: v1: 33 pages, 14 figures v2: 23 pages, 12 figures, revised to improve readability and make arguments more concise |
| Databáze: | arXiv |
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