Automorphism group of a group

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The 'automorphism group of a group $G$, denoted $Aut(G)$, is a set whose elements are automorphisms $\sigma:G \to G$, and where the group multiplication is composition of automorphisms. In other words, its group structure is obtained as a subgroup of $Sym(G)$, the group of all permutations on $G$.