Normalizer
- Page ID
- 19068
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Given a group G and one of its supergroups S, they are uniquely related to a third, intermediated group NS(G), called the normalizer of G with respect to S. NS(G) is defined as the set of all elements S ∈ S that map G onto itself by conjugation:
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- NS(G) := {S ∈S | S-1GS = G}
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The normalizer NS(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.