minimal normal subgroup

A **minimal normal subgroup** $K$ of a {{KNOWL('group', 'group')}} $G$ is a {{KNOWL('group.subgroup.normal', 'normal subgroup')}} of $G$ with the property that if $H \le K$ is normal in $G$ then either $H=K$ or $H=1$. Equivalently, $G / K$ is a {{KNOWL('group.maximal_quotient', 'maximal quotient')}} of $G$.