# Thompson's group F(n) is not minimally almost convex

@inproceedings{Wladis2007ThompsonsGF, title={Thompson's group F(n) is not minimally almost convex}, author={Claire Wladis}, year={2007} }

We prove that Thompson's group F (n) is not minimally almost convex with respect to the standard finite generating set. A group G with Cayley graph Γ is not minimally almost convex if for arbitrarily large values of m there exist elements g,h ∈ Bm such that dΓ(g,h )=2a nddBm (g,h )=2 m. (Here Bm is the ball of radius m centered at the identity.) We use tree-pair diagrams to represent elements of F (n) and then use Fordham's metric to calculate geodesic length of elements of F (n). Cleary and… Expand

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Unusual Geodesics in generalizations of Thompson's Group F

- Mathematics
- 2008

We prove that seesaw words exist in Thompson's Group F(N) for N=2,3,4,... with respect to the standard finite generating set X. A seesaw word w with swing k has only geodesic representatives ending… Expand

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… Expand

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

- Mathematics, Computer Science
- J. Lond. Math. Soc.
- 2012

A unique normal form for elements of F(n1, ..., nk) (with respect to the standard infinite generating set developed by Melanie Stein) is introduced which provides a solution to the word problem. Expand

Tree-pair Diagrams, the Word Problem, and the Metric for Generalizations of Thompson's Group F on more than One Integer

- Mathematics
- 2008

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… Expand

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