A group G is locally finite precisely when every bijective cellular automaton A^G to A^G is reversible for every alphabet A.
On a characterization of locally finite groups in terms of linear cellular automata
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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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math.GR 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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A Reversibility Characterization of Locally Finite Groups by Cellular Automata
A group G is locally finite precisely when every bijective cellular automaton A^G to A^G is reversible for every alphabet A.