Finite automata of polynomial growth do not generate a free group.

DOI10.1007/s10711-004-2368-0zbMath1075.20011OpenAlexW2083227394MaRDI QIDQ1768261

Xianqiang Yang

Publication date: 15 March 2005

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-004-2368-0

zbMATH Keywords

polynomial growthfree groupsfinite automataautomorphisms of treesregular rooted trees

Mathematics Subject Classification ID

Formal languages and automata (68Q45) Generators, relations, and presentations of groups (20F05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Groups acting on trees (20E08)

Related Items (14)

The true prosoluble completion of a group: examples and open problems. ⋮ On amenability of automata groups. ⋮ The groups of \(ZC\)-automaton transformations. ⋮ A commutator lemma for confined subgroups and applications to groups acting on rooted trees ⋮ The conjugacy problem in automaton groups is not solvable. ⋮ (Self-)similar groups and the Farrell-Jones conjectures. ⋮ Behaviors of entropy on finitely generated groups ⋮ On a family of Schreier graphs of intermediate growth associated with a self-similar group ⋮ On a class of poly-context-free groups generated by automata ⋮ 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 ⋮ Extensions of amenable groups by recurrent groupoids ⋮ TREE-WREATHING APPLIED TO GENERATION OF GROUPS BY FINITE AUTOMATA ⋮ Large scale properties for bounded automata groups.

Cites Work

• On the Burnside problem for periodic groups
• On Burnside's problem on periodic groups
• A just-nonsolvable torsion-free group defined on the binary tree
• Automorphisms of one-rooted trees: growth, circuit structure, and acyclicity.
• Wreath operations in the group of automorphisms of the binary tree
• TREE-WREATHING APPLIED TO GENERATION OF GROUPS BY FINITE AUTOMATA
• ON THE USE OF GRAPHS FOR COMPUTING A BASIS, GROWTH AND HILBERT SERIES OF ASSOCIATIVE ALGEBRAS
• The Generation of GL(n, Z) by Finite State Automata

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