A Thompson group for the basilica

Lecture 8 : Basilica group by Kate Juschenko

On a maximal subgroup of the Thompson simple group∗

The present paper deals with a maximal subgroup of the Thompson group, namely the group 2 + A9 := G. We compute its conjugacy classes using the coset analysis method, its inertia factor groups and Fischer matrices, which are required for the computations of the character table of G by means of Clifford-Fischer Theory. AMS subject classifications: 20C15, 20C40

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].

Some Remarks on the Braided Thompson Group BV

M. Brin and P.Dehornoy independently discovered a braided version BV of R.Thompson’s group V . In this paper, we discuss some properties of BV that might make the group interesting for group based cryptography. In particular, we show that BV does not admit a non-trivial linear representation.

Ideal structure of the C∗-algebra of Thompson group T

In a recent paper Uffe Haagerup and Kristian Knudsen Olesen show that for Richard Thompson’s group T , if there exists a finite set H which can be decomposed as disjoint union of sets H1 and H2 with ∑ g∈H1 π(g) = ∑ h∈H2 π(h) and such that the closed ideal generated by ∑ g∈H1 λ(g)− ∑ h∈H2 λ(h) coincides with C∗ λ(T ), then the Richard Thompson group F is not amenable. In particular, if C ∗ λ(T )...