Definition:Weakly Pronormal Subgroup/Definition 2
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Definition
Let $G$ be a group.
Let $H$ be a subgroup of $G$.
$H$ is weakly pronormal in $G$ if and only if:
- 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 $L$.