We describe under a variety of conditions abelian subgroups of the
automorphism group A of the regular n-ary tree T which are normalized by the
n-ary adding machine t=(e,...,e,t)s where s is the n-cycle (0,1,...,n-1). As an
application, for n a prime number, and for n = 4 we prove that every finitely
generated soluble subgroup of A containing t is an extension of a torsion-free
metabelian group by a finite group.