# Normalizer ^{ }

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### Dictionary Meaning and Definition on 'Normalizer'

**Normalizer Meaning and Definition**from

**WordNet (r) 2.0**

- normalizer
n : a person who normalizes [syn: normaliser]

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### Wikipedia Meaning and Definition on 'Normalizer'

In group theory, the centralizer and normalizer of a subset S of a group G are subgroups of G which have a restricted action on the elements of S and S as a whole, respectively. These subgroups can provide insight into the structure of G.

The centralizer of an element a of a group G (written as CG(a)) is the set of elements of G which commute with a; in other words, CG(a) = {x ∈ G : xa = ax}. If H is a subgroup of G, then CH(a) = CG(a) ∩ H. If there is no danger of ambiguity, we can write CG(a) as C(a). Another, less common, notation is sometimes used when there is no danger of ambiguity, namely, Z(a), which parallels the notation for the center of a group. With this latter notation, one must be careful to avoid confusion between the center of a group G, Z(G), and the centralizer of an element g in G, given by Z(g).

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