Virtual endomorphisms of nilpotent groups
Copyright policy )Virtual endomorphisms of nilpotent groups
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 G^φ when G is nilpotent. In particular, it is shown that if G is finitely generated, torsion-free and nilpotent then G^φ has solvability degree bounded above by the number of prime divisors of m .
- University of Brasília Brazil
- Universidade Federal de Mato Grosso Brazil
Subgroup theorems; subgroup growth, nilpotent groups, Group Theory (math.GR), Trees, Automorphisms of infinite groups, state-closed representations, subgroups of finite index, automorphisms of trees, Nilpotent groups, FOS: Mathematics, 20E08, 20F18, Groups acting on trees, virtual endomorphisms, Mathematics - Group Theory
Subgroup theorems; subgroup growth, nilpotent groups, Group Theory (math.GR), Trees, Automorphisms of infinite groups, state-closed representations, subgroups of finite index, automorphisms of trees, Nilpotent groups, FOS: Mathematics, 20E08, 20F18, Groups acting on trees, virtual endomorphisms, Mathematics - Group Theory
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