Commensurated subgroups in tree almost automorphism groups

Autor:	Boudec, Adrien Le, Wesolek, Phillip
Rok vydání:	2016
Předmět:	Mathematics - Group Theory
Druh dokumentu:	Working Paper
Popis:	We prove that the tree almost automorphism groups admit exactly three commensurability classes of closed commensurated subgroups. Our proof utilizes an independently interesting characterization of subgroups of the tree almost automorphism groups which contain only periodic elements in terms of the dynamics of the action on the boundary of the tree. Our results further cover several interesting finitely generated subgroups of the tree almost automorphism groups, including the Thompson groups $F$, $T$, and $V$. We show in particular that Thompson's group $T$ has no commensurated subgroups other than the finite subgroups and the entire group. As a consequence, we derive several rigidity results for the possible embeddings of these groups into locally compact groups. Comment: Accepted version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1604.04162 Zobrazit plný text záznamu View this record from Arxiv