In mathematics, a group is supersolvable (or supersoluble) if it has an invariant normal series where all the factors are cyclic groups.
G is supersolvable if there exists a normal series such that each quotient group
By contrast, for a solvable group the definition requires each quotient to be abelian.
In another direction, a polycyclic group must have a subnormal series with each quotient cyclic, but there is no requirement that each
As every finite solvable group is polycyclic, this can be seen as one of the key differences between the definitions.