normalized subgroup by another subgroup

Question

Let $A$ and $B$ be two subgroups of the same group $G$. What does it mean for the subgroup $A$ to be normalized by the subgroup $B$?

Answer 1

It means that for every $b\in B$, $A^b = \{b^{-1}ab\mid a\in A\} = A$. That is, that $B$ is a subgroup of the normalizer of $A$ in $G$.