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On a Characterization of Locally Finite Groups in Terms of Linear Cellular Automata
Tullio Ceccherini-Silberstein and Michel Coornaert

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.

Mathematical Subject Classification. 2000 20F50, 37B15, 68Q80

Keywords: Locally finite group, periodic group, cellular automaton, linear cellular automaton, Laplace operator

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