A Connected 3-State Reversible Mealy Automaton Cannot Generate an Infinite Burnside Group

DOI10.1007/978-3-319-21500-6_25zbMath1386.68106arXiv1409.6142OpenAlexW1858874872MaRDI QIDQ3451112

Dmytro Savchuk, Matthieu Picantin, Ines Klimann

Publication date: 10 November 2015

Published in: Developments in Language Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.6142

zbMATH Keywords

Burnside groupsautomaton groupsreversible Mealy automata

Mathematics Subject Classification ID

Periodic groups; locally finite groups (20F50) Algebraic theory of languages and automata (68Q70) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items (12)

Ergodic decomposition of group actions on rooted trees ⋮ To Infinity and Beyond ⋮ On bireversible Mealy automata and the Burnside problem ⋮ Orbit automata as a new tool to attack the order problem in automaton groups ⋮ An automaton group with undecidable order and Engel problems ⋮ On level-transitivity and exponential growth ⋮ A Connected 3-State Reversible Mealy Automaton Cannot Generate an Infinite Burnside Group ⋮ Automaton (Semi)groups: Wang Tilings and Schreier Tries ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On Torsion-Free Semigroups Generated by Invertible Reversible Mealy Automata ⋮ Boundary dynamics for bireversible and for contracting automaton groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Automata generating free products of groups of order 2.
• Orbit automata as a new tool to attack the order problem in automaton groups
• On the Burnside problem for periodic groups
• On Burnside's problem on periodic groups
• A geometric approach to (semi)-groups defined by automata via dual transducers.
• Freeness of automaton groups vs boundary dynamics
• Ergodic decomposition of group actions on rooted trees
• ON THE WORD AND PERIOD GROWTH OF SOME GROUPS OF TREE AUTOMORPHISMS
• On Torsion-Free Semigroups Generated by Invertible Reversible Mealy Automata
• Implementing Computations in Automaton (Semi)groups
• Some undecidability results for asynchronous transducers and the Brin-Thompson group $2V$
• CONJUGATION IN TREE AUTOMORPHISM GROUPS
• THE FINITENESS PROBLEM FOR AUTOMATON SEMIGROUPS IS UNDECIDABLE

This page was built for publication: A Connected 3-State Reversible Mealy Automaton Cannot Generate an Infinite Burnside Group