Subgroup Generated By An Element

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Definition (Subgroup Generated By An Element)

Let $G$ be a group and $a\in G$. Then the subgroup generated by $a$ is the set $$\langle a\rangle = \{a^n\mid n\in\mathbb{Z}\},$$ where we define $a^0=e$ and $a^{-n}=(a^{-1})^n$.

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