Given a group , embed in a larger group such that any automorphism of is the restriction of an inner automorphism of .

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# Outside in

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Given a group , embed in a larger group such that any automorphism of is the restriction of an inner automorphism of .

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Consider the semidirect product , which is called the

holomorphof and denoted . Obviously we have a copy of in and the product in is such that ; in other words, in the holomorph, conjugation of a group element by an automorphism amounts to evaluation.LikeLiked by 1 person