Abelian marginal subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed an abelian marginal subgroup if $$H$$ is an abelian group (i.e., it is an abelian subgroup of $$G$$) and $$H$$ is also a marginal subgroup of $$G$$.

Examples

 * The center in any group is an abelian marginal subgroup.
 * In a finite p-group $$G$$, the socle coincides with $$\Omega_1(Z(G))$$, the set of elements of order dividing $$p$$ in the center (see socle equals Omega-1 of center in nilpotent p-group). This is an abelian marginal subgroup.