A Proof that Thompson's Groups have Infinitely Many Relative Ends

2007/08/09 by Daniel Farley, Farley, Daniel
Mathematics · #20F69 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F69

paper · pdf · doi:10.48550/arxiv.0708.1334

11 pages, 1 figure

arxiv created 2007/08/09 · arxiv updated 2009/12/01

Abstract

We show that each of Thompson's groups F, T, and V have infinitely many ends relative to certain subgroups. We go on to show that T and V both have Serre's property FA, i.e., any action of T or V on a tree will have a fixed point. (The proof of the latter statement was originally due to Ken Brown, and our proof is based on his notes.)

Related

• A short account of why Thompson's group F is of type\n textrmF_\∞
• The Maximality of T in Thompson's group V
• Twisted conjugacy classes in R. Thompson's group F
• The conjugacy problem in extensions of Thompson's group F
• Conjugacy, roots, and centralizers in Thompson's group F