High Quality Content by WIKIPEDIA articles! In mathematics, a group is supersolvable (or supersoluble) if it has an invariant normal series where all the factors are cyclic groups. Supersolvablility is stronger than the notion of solvability. Some facts about supersolvable groups: Supersolvable groups are always polycyclic, and hence solvable. Every finitely generated nilpotent group is supersolvable.Every metacyclic group is supersolvable. The commutator subgroup of a supersolvable group is nilpotent. Subgroups and quotient groups of supersolvable groups are supersolvable.

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