Virtual endomorphisms of nilpotent groups

  • Adilson A. Berlatto

    Universidade Federal de Mato Grosso, Pontal Do Araguaia, Brazil
  • Said N. Sidki

    Universidade de Brasília, Brazil


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