Corpus ID: 117709954

Nonassociative Ramsey Theory and the amenability of Thompson's group

@article{Moore2012NonassociativeRT,
  title={Nonassociative Ramsey Theory and the amenability of Thompson's group},
  author={Justin Tatch Moore},
  journal={arXiv: Group Theory},
  year={2012}
}
  • J. Moore
  • Published 2012
  • Mathematics
  • arXiv: Group Theory
The purpose of this article is prove that Thompson's group F is amenable. The methods developed will then be used to prove a generalization of Hindman's theorem for the free nonassociative binary system on one generator. 
Idempotent means on free binary systems do not exist
Free binary systems are shown to not admit idempotent means. This refutes a conjecture of the author. It is also shown that the extension of Hindman's theorem to nonassociative binary systemsExpand
Thompson’s Group F
R. Thompson’s group F is introduced and explored. Its elements are described as equivalence classes of tree diagrams and also as continuous piecewise linear functions from the unit interval toExpand
On the stabilizers of finite sets of numbers in the R. Thompson group $F$
We study subgroups $H_U$ of the R. Thompson group $F$ which are stabilizers of finite sets $U$ of numbers in the interval $(0,1)$. We describe the algebraic structure of $H_U$ and prove that theExpand

References

SHOWING 1-10 OF 39 REFERENCES
Amenability and Ramsey Theory
The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey theoretic reformulation of amenability constitutesExpand
THE THOMPSON GROUP F IS AMENABLE
Amenability of some discrete subgroups of the group of diffeomorphisms of interval is proved. As a consequence, a solution of the problem of amenability of the Thompson group F is given.
Fast growth in the Følner function for Thompson’s group $F$
The purpose of this note is to prove a lower bound on the growth of Folner functions for Thompson’s group F . Specifically I will prove that, for any finite generating set Γ ⊆ F , there is a constantExpand
Amenability via random walks
We use random walks to show that the Basilica group is amenable, answering an open question of Grigorchuk and ˙ Zuk. Our results separate the class of amenable groups from the closure ofExpand
A note on Shavgulidze's papers concerning the amenability problem for Thompson's group $F$
This paper examines Shavgulidze's postings to the ArXiv and publications which concern his argument that Thompson's group F is amenable. In particular I list specific places where there are errors inExpand
Finite Sums from Sequences Within Cells of a Partition of N
  • N. Hindman
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1974
TLDR
The principal result of this paper establishes the validity of a conjecture that, if the natural numbers are divided into two classes, then there is a sequence drawn from one of those classes such that all finite sums of distinct members of that sequence remain in the same class. Expand
On a Torsion-Free Weakly Branch Group Defined by a Three State Automaton
We study a torsion free weakly branch group G without free subgroups defined by a three state automaton which appears in different problems related to amenability, Galois groups and monodromy. Here...
Non-amenable finitely presented torsion-by-cyclic groups
We construct a finitely presented non-amenable group without free non-cyclic subgroups thus providing a finitely presented counterexample to von Neumann's problem. Our group is an extension of aExpand
Entropy and isoperimetry for linear and non-linear group actions
We prove inequalities of isoperimetric type for groups acting on linear spaces and discuss related geometric and combinatorial problems, where we use the Boltzmann entropy to keep track of theExpand
Amenability of discrete subgroups of the group of diffeomorphisms of the circle
The amenability of several discrete subgroups of the group of diffeomorphisms of the circle is proved.
...
1
2
3
4
...