Group with nilpotent derived subgroup

Definition
A group with nilpotent commutator subgroup, also called a nilpotent-by-abelian group, is a group satisfying the following equivalent conditions:


 * Its fact about::commutator subgroup is a fact about::nilpotent group.
 * It has a fact about::nilpotent normal subgroup with an abelian quotient group.
 * It has a fact about::nilpotent characteristic subgroup with an abelian quotient group.

Stronger properties

 * Weaker than::Supersolvable group
 * Weaker than::Nilpotent group
 * Weaker than::Metabelian group

Weaker properties

 * Stronger than::Group satisfying subnormal join property: