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Problem ($\text{Inn}(G)$ is a normal subgroup of $\text{Aut}(G)$)
Let $G$ be a group. Prove the following:
- $\text{Aut}(G)$ is a group,
- $\text{Inn}(G)$ is a subgroup of $\text{Aut}(G)$, and
- $\text{Inn}(G)$ is a normal subgroup of $\text{Aut}(G)$.
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