# normalizer

## English

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### Noun

normalizer (plural normalizers)

1. one who normalizes, fits to a norm or standard etc.
2. (algebra) The subset of elements of some group which leave some given subset invariant when conjugating it.
In symbols, the normalizer of some subset ${\displaystyle S}$ of group ${\displaystyle G}$ is the subset ${\displaystyle N(S)=\{g\in G|g^{-1}Sg=S\}}$, so that ${\displaystyle S}$ would be a normal subgroup if ${\displaystyle N(S)}$ were the whole group.