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    Aut(G), the set of automorphisms of G, is also a group.

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    Modern Algebra
    Group Theory (LXX)
    The Set of all Automorphisms of a Group

    If G is a group, then Aut(G), the set of automorphisms of G, is also a group.

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    Modern Algebra
    Group Theory (LXX)
    The Set of all Automorphisms of a Group

    By:- Thokchom Sarojkumar Sinha

    If is a group, then , the set of automorphisms of , is also a group.

    Solution:- Let be arbitrary.

    Closure Property

    are one-one onto
    is one-one onto.

    For all ,

    and

    Then

    Thus

    Hence

    Associativity

    ...

    Solution Summary

    It is proven that if G is a group, then Aut(G), the set of automorphisms of G, is also a group. The solution is detailed and well presented.

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