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On a characterization of locally finite groups in terms of linear cellular automata

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arxiv 0906.4891 v1 pith:GFMWAZMQ submitted 2009-06-26 math.GR math.DS

Tullio Ceccherini-Silberstein , Michel Coornaert This is my paper · ORCID
classification math.GRmath.DS
keywords cellularfinitelinearlocallyalphabetautomataautomatoncharacterization
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abstract

We prove that a group $G$ is locally finite if and only if every surjective real (or complex) linear cellular automaton with finite-dimensional alphabet over $G$ is injective.

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  1. A Reversibility Characterization of Locally Finite Groups by Cellular Automata

    math.GR 2026-06 unverdicted novelty 8.0 of 10

    A group G is locally finite precisely when every bijective cellular automaton A^G to A^G is reversible for every alphabet A.

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