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.
1
Universidade Federal de Mato Grosso, Pontal Do Araguaia, Brazil
2
Universidade de Brasília, Brazil
Adilson A. Berlatto; Said N. Sidki. Virtual endomorphisms of nilpotent groups. Groups, geometry, and dynamics, Tome 1 (2007) no. 1, pp. 21-46. doi: 10.4171/ggd/2
@article{10_4171_ggd_2,
author = {Adilson A. Berlatto and Said N. Sidki},
title = {Virtual endomorphisms of nilpotent groups},
journal = {Groups, geometry, and dynamics},
pages = {21--46},
year = {2007},
volume = {1},
number = {1},
doi = {10.4171/ggd/2},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/2/}
}
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AU - Adilson A. Berlatto
AU - Said N. Sidki
TI - Virtual endomorphisms of nilpotent groups
JO - Groups, geometry, and dynamics
PY - 2007
SP - 21
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IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/2/
DO - 10.4171/ggd/2
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