finite group

《代数学引论》 · 第 27 页

如果 $|G|$ 是一有限数，即 $G$ 只含有有限多个元素，$G$ 就称为有限群；如果 $G$ 含有无限多个元素，$G$ 就称为无限群。

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《Abstract Algebra》 · 第 17 页 · Section 1.1「Basic Axioms and Examples」

We shall immediately become less formal and say $G$ is a group under $*$ if $(G,*)$ is a group (or just $G$ is a group when the operation $*$ is clear from the context). Also, we say $G$ is a finite group if in addition $G$ is a finite set.