Definition:Weakly Pronormal Subgroup/Definition 2

Definition
Let $G$ be a group.

Let $H$ be a subgroup of $G$.

$H$ is weakly pronormal in $G$ :
 * if $H \le K \le L \le G$ are such that $K$ is a normal subgroup of $L$, then $K N_L \left({H}\right) = L$

where:
 * $H \le K$ denotes that $H$ is a subgroup of $K$
 * $N_L \left({H}\right)$ denotes the normalizer of $H$ in $L$.

Also see

 * Equivalence of Definitions of Weakly Pronormal Subgroup