  A virtual endomorphism of a group G is a homomorphism f from H into G where H
is a subgroup of G of finite index m. The triple (G,H,f) produces a
state-closed (or, self-similar) representation t of G on the 1-rooted m-ary
tree. This paper is a study of properties of the image G^t when G is nilpotent.
In particular, it is shown that if G is finitely generated, torsion-free and
nilpotent then G^t has solvability degree bounded above by the number of prime
divisors of m.
