The word problem and the metric for the Thompson-Stein groups

Details The word problem and the metric for the Thompson-Stein groups The word problem and the metric for the Thompson-Stein groups

2008-11-19

arxiv.org/abs/0811.3036v2

Mathematics

Group Theory

v1: 33 pages, 14 figures v2: 23 pages, 12 figures, revised to improve readability and make arguments more concise

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The word problem and the metric for the Thompson-Stein groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The word problem and the metric for the Thompson-Stein groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The word problem and the metric for the Thompson-Stein groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-428903