A virtual endomorphism of a group G is a homomorphism f : H→ 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 φ of G on the 1-rooted m-ary tree. This paper is a study of properties of the image Gφ when G is nilpotent. In particular, it is shown that if G is finitely generated, torsion-free and nilpotent then Gφ has solvability degree bounded above by the number of prime divisors of m.
Cite this article
Adilson A. Berlatto, Said N. Sidki, Virtual endomorphisms of nilpotent groups. Groups Geom. Dyn. 1 (2007), no. 1, pp. 21–46DOI 10.4171/GGD/2