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Reply To: Maths


What do you call a set/group whose automorphisms are its own members?

[A paradox in waiting? For a group, each element gives an automorphism by conjugation. The automorphism is trivial if and only if the element commutes with everything in the group, so this identification of elements with automorphisms gives an injective map from G to Aut G precisely when G has trivial centre. The question is then whether there are any other automorphisms. If G has trivial centre and no outer automorphisms it is isomorphic to its own automorphism group, and is said to be complete. Harry]

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