Abstract commensurators of
groups acting on rooted trees

by Claas Röver

Keywords

commensurators, finitely presented simple groups, automorphisms of trees

Abstract

This note is concerned with groups which act on locally finite spherically homogeneous rooted trees. I give conditions under which the abstract commensurator is isomorphic to the relative commensurator inside the homeomorphism group of the boundary of the tree.

I also prove that, if G is an infinte group which is commensurable with its on n-th direct power for some n>1, the abstract commensurator of G contains a Higman-Thompson group as a subgroup.

This plus some extra work enables me to determine the abstract commensurator C of ‘the’ Grigorchuk 2-group. In particular, it is shown that C is a finitely presented (infinite) simple group.

This is published in Geom. Dedicata 94 (2002), 45-61

Of course you can also ask me for a copy.