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Math Help - Prove that I(G) is normal in A(G)

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    Prove that I(G) is normal in A(G)

    For any group G prove that I(G) is a normal subgroup of A(G).

    Where I(G) denotes the group of inner automorphisms and A(G) denotes the group of automorphisms on a group G.

    Thanks and Regards,
    Kalyan.
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    Quote Originally Posted by kalyanram View Post
    For any group G prove that I(G) is a normal subgroup of A(G).

    Where I(G) denotes the group of inner automorphisms and A(G) denotes the group of automorphisms on a group G.

    Thanks and Regards,
    Kalyan.

    If I_g\in I(G) (\,\,i.e.\,,\,I_g(x):=gxg^{-1}\,\,\forall x\in G)\,,\,\,then\,\,\forall \phi\in A(G)\,,\,\,\phi^{-1}I_g\phi=I_{\phi^{-1}(g)}

    Tonio
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