Finite supersolvable group

Definition
A finite supersolvable group is a finite group satisfying the following equivalent conditions:


 * 1) It is a defining ingredient::supersolvable group: it has a normal series where all the quotients are cyclic groups.
 * 2) It has a defining ingredient::chief series where all the successive quotients are groups of prime order.
 * 3) It is a defining ingredient::solvable group that also satisfies the property that its chief series are composition series.

Stronger properties

 * Weaker than::Finite abelian group
 * Weaker than::Finite nilpotent group

Weaker properties

 * Stronger than::Group having subgroups of all orders dividing the group order:
 * Stronger than::Finite solvable group