Virtual endomorphisms of nilpotent groups.

DOI10.4171/GGD/2zbMath1128.20016arXivmath/0602131OpenAlexW2018624566MaRDI QIDQ2372587

Yanyan Li

Publication date: 31 July 2007

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0602131

zbMATH Keywords

subgroups of finite indexnilpotent groupsautomorphisms of treesvirtual endomorphismsstate-closed representations

Mathematics Subject Classification ID

Trees (05C05) Subgroup theorems; subgroup growth (20E07) Nilpotent groups (20F18) Automorphisms of infinite groups (20E36) Groups acting on trees (20E08)

Related Items (16)

On the self-similarity index of \(p\)-adic analytic pro-\(p\) groups ⋮ Affine automorphisms of rooted trees ⋮ On hereditarily self-similar \(p\)-adic analytic pro-\(p\) groups ⋮ Finite-state self-similar actions of nilpotent groups. ⋮ Arithmetic aspects of self-similar groups. ⋮ Self-similar abelian groups and their centralizers ⋮ Graph-directed systems and self-similar measures on limit spaces of self-similar groups ⋮ On state-closed representations of restricted wreath product of groups \(G_{p,d}=C_{p}wrC^{d}\) ⋮ Self-similarity of some soluble relatively free groups ⋮ Intransitive self-similar groups ⋮ Abelian state-closed subgroups of automorphisms of \(m\)-ary trees. ⋮ Self-similar groups of type \(FP_n\) ⋮ On self-similar Lie algebras and virtual endomorphisms ⋮ Almost-automorphisms of trees, cloning systems and finiteness properties ⋮ On self-similar finite \(p\)-groups ⋮ On self-similarity of \(p\)-adic analytic pro-\(p\) groups of small dimension

Cites Work

• A free group of finite automata
• Automorphisms of one-rooted trees: growth, circuit structure, and acyclicity.
• Automata and square complexes.
• On a free group of transformations defined by an automaton.
• Compressibility in Nilpotent Groups
• The Generation of GL(n, Z) by Finite State Automata
• ON CO-HOPFIAN NILPOTENT GROUPS
• Endomorphisms of Compact Differentiable Manifolds
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