An exploration of normalish subgroups of R. Thompson's groups F and T

2016/03/05 by Bleak, Collin
#20E07 #46L05 #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1603.01726

Abstract

In this short note, we show that R. Thompson's group F admits a normalish amenable subgroup, and that the standard copy of F in R. Thompson's group T is normalish in T. We further conjecture that if F is non-amenable, then T does not admit a normalish amenable subgroup, and therefore that the reduced C^* algebra of T is in fact simple in that case.

Related

• Non-inner amenability of the Thompson groups T and V
• Subgroups of R. Thompson's Group F that are Isomorphic to F
• Non-amenability of R.Thompson's group F
• The Inner Amenability of the Generalized Thompson Group
• Computational explorations of the Thompson group T for the amenability problem of F