generator

《代数学引论》 · 第 61 页

如果 $\langle S\rangle=G$，那么 $S$ 就称为 $G$ 的一组生成元。

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《Abstract Algebra》 · 第 54 页 · Section 2.3「Cyclic Groups and Cyclic Subgroups」，Definition 后

A group $H$ is cyclic if $H$ can be generated by a single element, i.e., there is some element $x\in H$ such that $H=\{x^n\mid n\in\mathbb Z\}$. In additive notation $H$ is cyclic if $H=\{nx\mid n\in\mathbb Z\}$. In both cases we shall write $H=\langle x\rangle$ and say $H$ is generated by $x$ (and $x$ is a generator of $H$).