# The word problem and the metric for the Thompson–Stein groups

@article{Wladis2012TheWP, title={The word problem and the metric for the Thompson–Stein groups}, author={Claire Wladis}, journal={Journal of the London Mathematical Society}, year={2012}, volume={85} }

We consider the Thompson–Stein group F(n1,…,nk), where n1, …, nk∈{2, 3, 4, …} and k∈ℕ. 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(n1,…,nk), and we prove several theorems describing the equivalence of trees and tree‐pair diagrams. We introduce a unique normal form for elements of F(n1…

## 3 Citations

### The BNSR-invariants of the Stein group 𝐹2,3

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- 2021

Abstract The Stein group F 2 , 3 F_{2,3} is the group of orientation-preserving piecewise linear homeomorphisms of the unit interval with slopes of the form 2 p 3 q 2^{p}3^{q} ( p , q ∈ Z…

### The automorphism group of Thompson's group F: subgroups and metric properties.

- Mathematics
- 2011

We describe some of the geometric properties of the automorphism group Aut(F) of Thompson's group F. We give realizations of Aut(F) geometrically via periodic tree pair diagrams, which lead to…

### THOMPSON'S GROUP IS DISTORTED IN THE THOMPSON-STEIN GROUPS

- Mathematics
- 2011

We show that the inclusion map of the generalized Thompson groups F(n i ) is exponentially distorted in the Thompson―Stein groups F(n 1 , ... , n k ) for k > 1. One consequence is that F is…

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