Dedekind normal subgroup

Definition
A subgroup of a group is termed a Dedekind normal subgroup if it satisfies the following two conditions:


 * It is a normal subgroup of the group.
 * It is a Dedekind group: every subgroup of it is normal in it.

Stronger properties

 * Weaker than::Central subgroup
 * Weaker than::Cyclic normal subgroup
 * Weaker than::Abelian normal subgroup
 * Weaker than::Hereditarily normal subgroup
 * Weaker than::Subgroup contained in the Baer norm

Weaker properties

 * Stronger than::Nilpotent normal subgroup
 * Stronger than::Solvable normal subgroup
 * Stronger than::Hereditarily 2-subnormal subgroup
 * Stronger than::Right-transitively 2-subnormal subgroup
 * Stronger than::Normal subgroup