Algorithmic Decidability of Engel’s Property for Automaton Groups

DOI10.1007/978-3-319-34171-2_3zbMath1477.20067arXiv1512.01717OpenAlexW3099996731MaRDI QIDQ5740175

Laurent Bartholdi

Publication date: 25 July 2016

Published in: Computer Science – Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.01717

Mathematics Subject Classification ID

Formal languages and automata (68Q45) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Engel conditions (20F45) Computational methods for problems pertaining to group theory (20-08)

Related Items (9)

Numerical upper bounds on growth of automaton groups ⋮ An automaton group with undecidable order and Engel problems ⋮ Bounded Engel elements in groups satisfying an identity ⋮ Engel elements in weakly branch groups ⋮ Algorithmic problems in Engel groups and cryptographic applications ⋮ A note on Engel elements in the first Grigorchuk group ⋮ Engel elements in some fractal groups ⋮ A New Hierarchy for Automaton Semigroups ⋮ Commutator width in the first Grigorchuk group

Uses Software

• GAP
• FR

Cites Work

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• Geometry and arithmetic of verbal dynamical systems on simple groups (with an appendix by Nathan Jones)
• The Engel elements of a soluble group
• Iterated identities and iterational depth of groups
• On compact Engel groups.
• On locally finite varieties with undecidable equational theory.
• On Torsion-Free Semigroups Generated by Invertible Reversible Mealy Automata
• Implementing Computations in Automaton (Semi)groups
• The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable
• THE FINITENESS PROBLEM FOR AUTOMATON SEMIGROUPS IS UNDECIDABLE
• GROUP LAWS AND FREE SUBGROUPS IN TOPOLOGICAL GROUPS

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