If $H$ is a subgroup of a group $G$, the **normal closure** of $H$ is the smallest normal subgroup of $G$ containing $H$. Alternatively, it is the subgroup generated by the set
$$ \bigcup_{g\in G} gHg^{-1}. $$

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**Knowl status:**

- Review status: beta
- Last edited by John Jones on 2019-06-10 15:54:02

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