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Virtual Endomorphisms of Nilpotent Groups

Adilson Berlatto·Said Sidki
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Abstract

A virtual endomorphism of a group G is a homomorphism f from H into 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 t of G on the 1-rooted m-ary tree. This paper is a study of properties of the image G^t when G is nilpotent. In particular, it is shown that if G is finitely generated, torsion-free and nilpotent then G^t has solvability degree bounded above by the number of prime divisors of m.

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Adilson Berlatto, Said Sidki. 2006-10-12. Virtual Endomorphisms of Nilpotent Groups. https://arxiv.org/abs/math/0602131

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