Virtual endomorphisms of nilpotent groups
Adilson A. Berlatto
Universidade Federal de Mato Grosso, Pontal Do Araguaia, BrazilSaid N. Sidki
Universidade de Brasília, Brazil

Abstract
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. 21–46
DOI 10.4171/GGD/2