1.73: Normalizer
Given a group G and one of its supergroups S, they are uniquely related to a third, intermediated group N S (G), called the normalizer of G with respect to S . N S (G) is defined as the set of all elements S ∈ S that map G onto itself by conjugation:
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- N S (G) := { S ∈S | S -1 GS = G}
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The normalizer N S (G) may coincide either with G or with S or it may be a proper intermediate group. In any case, G is a normal subgroup of its normalizer.