Definition:Weakly Abnormal Subgroup/Definition 1

Definition
Let $G$ be a group.

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

$H$ is weakly abnormal in $G$ :


 * $\forall g \in G: g \in H^{\left\langle{g}\right\rangle}$

where $H^{\left\langle{g}\right\rangle}$ denotes the smallest subgroup of $G$ containing $H$, generated by the conjugacy action by the cyclic subgroup of $G$ generated by $g$.

Also see

 * Equivalence of Definitions of Weakly Abnormal Subgroup