Lattice of normal subgroups of a group of local isometries of the boundary of a spherically homogeneous tree

Abstract

We describe the structure of the lattice of normal subgroups of the group of local isometries of the boundary of a spherically homogeneous tree LIsom ∂T. It is proved that every normal subgroup of this group contains its commutant. We characterize the quotient group of the group LIsom ∂T by its commutant.