1.NounOne who or that which normalizes, fits to a norm or standard etc.
2.NounThe 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."