Last Updated：2025/11/30

(mathematics) A group such that every injective cellular automaton with the group elements as its cells is also surjective.

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surjunctive group

Source Word

surjunctive group

Noun

(mathematics) A group such that every injective cellular automaton with the group elements as its cells is also surjective.

Japanese Meaning

数学的用語。細胞オートマトン（その細胞に群の元を用いる）が単射ならば必ず全射となるという性質を持つ群のこと。

Proving that a given group is a surjunctive group often requires combining dynamical, algebraic, and combinatorial techniques.

与えられた群が、その群上の任意の単射なセルラーオートマトンが必ず全射になる群であることを証明するには、多くの場合、動的、代数的、組合せ的な手法を組み合わせる必要がある。

Sense（1）

(mathematics) A group such that every injective cellular automaton with the group elements as its cells is also surjective.

We prove that pre-injective, post-surjective cellular automata over surjunctive groups are reversible.

surjunctive groups

（ plural ）