Normalizing subgroup

Definition
Let $$H$$ and $$K$$ be subgroups of a group $$G$$. We say that $$H$$ is a normalizing subgroup for $$K$$ if the following equivalent conditions are satisfied:


 * For every $$h \in H$$, $$hKh^{-1} = K$$
 * $$H \le N_G(K)$$, viz, $$H$$ is contained in the normalizer of $$K$$