Free subgroups in groups acting on rooted trees

DOI10.4171/GGD/110zbMath1267.37009arXiv0802.2554MaRDI QIDQ531921

Volodymyr V. Nekrashevych

Publication date: 21 April 2011

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

Full work available at URL: https://arxiv.org/abs/0802.2554

zbMATH Keywords

free groupsactions on treesself-similar groupsgerms of actions

Mathematics Subject Classification ID

Geometric group theory (20F65) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Dynamical systems involving maps of trees and graphs (37E25) Groups acting on trees (20E08)

Related Items

LOCALLY NORMAL SUBGROUPS OF TOTALLY DISCONNECTED GROUPS. PART I: GENERAL THEORY, A commutator lemma for confined subgroups and applications to groups acting on rooted trees, A finitely generated branch group of exponential growth without free subgroups., The conjugacy problem in automaton groups is not solvable., On a family of Schreier graphs of intermediate growth associated with a self-similar group, Some topics in the dynamics of group actions on rooted trees., Growth of Schreier graphs of automaton groups., Endomorphisms of regular rooted trees induced by the action of polynomials on the ring ℤd of d-adic integers, Schreier graphs of an extended version of the binary adding machine., On some universal construction of minimal topological generating sets for inverse limits of iterated wreath products of non-abelian finite simple groups, Amenable groups without finitely presented amenable covers, Subgroup dynamics and $C^\ast$-simplicity of groups of homeomorphisms, Generic properties in some classes of automaton groups, Fragile words and Cayley type transducers, Extensions of amenable groups by recurrent groupoids

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On amenability of automata groups.
• On Burnside's problem on periodic groups
• The ubiquity of free subgroups in certain inverse limits of groups
• Cyclic renormalization and automorphism groups of rooted trees
• Automata and square complexes.
• Boundary behavior for groups of subexponential growth.
• \(\omega\)-periodic graphs
• Dimension and randomness in groups acting on rooted trees
• DEGREES OF GROWTH OF FINITELY GENERATED GROUPS, AND THE THEORY OF INVARIANT MEANS
• The Generation of GL(n, Z) by Finite State Automata