Group cellular automata are continuous, shift-commuting endomorphisms of $G^\mathbb{Z}$, where $G$ is a finite group. We provide an easy-to-check characterization of expansivity for group cellular automata on abelian groups and we prove that expansivity is a decidable property for general (non-abelian) groups. Moreover, we show that the class of expansive group cellular automata is strictly contained in that of topologically transitive injective group cellular automata.

翻译：群元胞自动机是 $G^\mathbb{Z}$ 上的连续、平移交换自同态，其中 $G$ 为有限群。我们针对阿贝尔群上的群元胞自动机给出了一个易于检验的可扩展性特征刻画，并证明对于一般（非阿贝尔）群而言，可扩展性是可判定的性质。此外，我们证明了可扩展群元胞自动机类严格包含于拓扑传递的单射群元胞自动机类之中。