Corpus ID: 9764857

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

  title={Thompson's group F(n) is not minimally almost convex},
  author={Claire Wladis},
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
Unusual Geodesics in generalizations of Thompson's Group F
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 endingExpand
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The word problem and the metric for the Thompson-Stein groups
  • Claire Wladis
  • 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
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Abstract We show that Thompson's group F does not satisfy Cannon's almost convexity condition AC ( n ) for any positive integer n with respect to the standard generating set with two elements. ToExpand
Automorphisms of Generalized Thompson Groups
0.1. Results. We study the automorphisms of some generalizations of Thompson’s groups and their underlying structures. The automorphism groups of two of Thompson’s original groups were analyzed inExpand
Minimal almost convexity
Abstract In this article we show that the Baumslag–Solitar group BS(1, 2) is minimally almost convex, or MAC. We also show that BS(1, 2) does not satisfy Poénaru’s almost convexity condition P(2),Expand
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We introduce forest diagrams to represent elements of Thompson's group F. These diagrams relate to a certain action of F on the real line in the same way that tree diagrams relate to the standardExpand
Dead end words in lamplighter groups and other wreath products
We explore the geometry of the Cayley graphs of the lamplighter groups and a wide range of wreath products. We show that these groups have dead end elements of arbitrary depth with respect to theirExpand
An Elementary Construction of Unsolvable Word Problems in Group Theory
Publisher Summary This chapter presents an elementary construction of unsolvable word problems in group theory and introduces a new approach to constructing finitely presented groups with unsolvableExpand
A note on the Ponaru condition
Thompson's group F is maximally nonconvex
  • Contemp. Math
  • 2005
Introductory notes on Richard Thompson's groups
  • MR1426438 (98g:20058), Zbl 0880
  • 1996
Almost convex groups