Definition:Weakly Abnormal Subgroup/Definition 1

Definition

Let $G$ be a group.

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

$H$ is weakly abnormal in $G$ if and only if:

$\forall g \in G: g \in H^{\gen g}$

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

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Also see

• Equivalence of Definitions of Weakly Abnormal Subgroup