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

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