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

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. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1350–1356, October, 2008.