Amenability problem for Thompson's group \(F\): state of the art

Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Geometric group theory (20F65) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Ore rings, multiplicative sets, Ore localization (16U20)

Cites Work

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Fast growth in the Følner function for Thompson's group \(F\).
A partial converse to a theorem of Tamari.
An infinite-dimensional torsion-free \(\text{FP}_{\infty}\) group
Amenable semigroups
Ruinous subsets of Richard Thompson's group \(F\).
Testing Cayley graph densities.
Groups of piecewise linear homeomorphisms of the real line
Elementary amenable groups
Introductory notes on Richard Thompson's groups
Non-amenable finitely presented torsion-by-cyclic groups.
Über eine Schlußweise aus dem Endlichen ins Unendliche.
Zur allgemeinen Theorie des Maßes.
Amenability of semigroups and the Ore condition for semigroup rings
On groups with full Banach mean value
Full Banach Mean Values on Countable groups.
Symmetric Random Walks on Groups
An example of a finitely presented amenable group not belonging to the classEG
ON THE PROBLEM OF THE EXISTENCE OF AN INVARIANT MEAN ON A GROUP
Diagram groups
Amenability and paradoxical decompositions for pseudogroups and for discrete metric spaces
ON THE PROPERTIES OF THE CAYLEY GRAPH OF RICHARD THOMPSON'S GROUP F
Automaticity, goals, and environmental interactions.
On the density of Cayley graphs of R.Thompson’s group F in symmetric generators
Systems of equations over the group ring of Thompson’s group F
R. Thompson’s group and the amenability problem
On the Ore condition for the group ring of R. Thompson’s group F
Combinatorial Algebra: Syntax and Semantics
A Minimal Candidate for the Existence of a Weakly-Ruinous Set
Evacuation schemes on Cayley graphs and non-amenability of groups
Finiteness properties of groups

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