Fully normalized subgroup

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In mathematics, in the field of group theory, a subgroup of a group is said to be fully normalized if every automorphism of the subgroup lifts to an inner automorphism of the whole group. Another way of putting this is that the natural embedding from the Weyl group of the subgroup to its automorphism group is surjective.

In symbols, a subgroup is fully normalized in if, given an automorphism of , there is a such that the map , when restricted to is equal to .

Some facts:

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