2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108877A 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.21 pages Modification of the original textGroup Theory20E08, 20F18text