Normalizer

Noun

1. One who or that which normalizes, fits to a norm or standard etc.
2. The subset of elements of some group which leave some given subset invariant when conjugating it.

   "In symbols, the normalizer of some subset S {\displaystyle S} of group G {\displaystyle G} is the subset N ( S ) = { g ∈ G | g − 1 S g = S } {\displaystyle N(S)=\{g\in G|g^{-1}Sg=S\}} , so that S {\displaystyle S} would be a normal subgroup if N ( S ) {\displaystyle N(S)} were the whole group."