cyclic group

《代数学引论》 · 第 61 页

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

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 $H=\{x^n\mid n\in\mathbb Z\}$ (where as usual the operation is multiplication).