Category:Abnormal Subgroups

This category contains results about Abnormal Subgroups.

Let $G$ be a group.

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

Then $H$ is an abnormal subgroup if and only if:

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

where $\gen {H, H^g}$ is the subgroup of $G$ generated by $H$ and the conjugate of $H$ by $g$.