منابع مشابه
Convexity Properties of Thompson ’ S Group F
We prove that Thompson's group F is not minimally almost convex with respect to any generating set which is a subset of the standard infinite generating set for F and which contains x1. We use this to show that F is not almost convex with respect to any generating set which is a subset of the standard infinite generating set, generalizing results in [HST].
متن کاملThompson ’ s group F ( n ) is not minimally almost convex
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) = 2 and dBm (g, h) = 2m. (Here Bm is the ball of radius m centered at the identity.) We use tree-pair diagrams to represent eleme...
متن کاملThompson ’ S Group F Is Not Almost Convex
We show that Thompson’s group F does not satisfy Cannon’s almost convexity condition AC(n) for any integer n in the standard finite two generator presentation. To accomplish this, we construct a family of pairs of elements at distance n from the identity and distance 2 from each other, which are not connected by a path lying inside the n-ball of length less than k for increasingly large k. Our ...
متن کاملQuasi - Isometrically Embedded Subgroups of Thompson ’ S Group F 3
The goal of this paper is to construct quasi-isometrically embedded subgroups of Thompson’s group F which are isomorphic to F × Zn for all n. A result estimating the norm of an element of Thompson’s group is found. As a corollary, Thompson’s group is seen to be an example of a finitely presented group which has an infinite-dimensional asymptotic cone. The interesting properties of Thompson’s gr...
متن کاملT C C F
We review links between three logic formalisms and three approaches to specifying operational semantics. In particular, we show that specifications written with (small-step and big-step) SOS, abstract machines, and multiset rewriting, are closely related to Horn clauses, binary clauses, and (a subset of) linear logic, respectively. We shall illustrate how binary clauses form a bridge between th...
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ژورنال
عنوان ژورنال: Nature
سال: 1937
ISSN: 0028-0836,1476-4687
DOI: 10.1038/140610b0