A normalizer is a part of a group.
Let be a subset of a group . An element of is said to normalize if . A subset of is said to normalize if all its elements normalize . The set of all elements of that normalize is called the normalizer of . It is often denoted as , or , when there is no risk of confusion. It is evidently a subgroup of ; for ; if normalize , then and if , then . Evidently, .
When is a subgroup of , is the largest subgroup of of which is a normal subgroup.
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