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

Michel Coornaert; Tullio Ceccherini-Silberstein

arxiv: 0906.4891 · v1 · pith:GFMWAZMQnew · submitted 2009-06-26 · 🧮 math.GR · math.DS

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

Tullio Ceccherini-Silberstein , Michel Coornaert This is my paper

classification 🧮 math.GR math.DS

keywords cellularfinitelinearlocallyalphabetautomataautomatoncharacterization

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

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