supersolvable group

A group $G$ is supersolvable if it has a finite normal series

G=G_{0}\\rhd G_{1}\\rhd\\cdots\\rhd G_{n}=1

with the property that each factor group $G_{i-1}/G_{i}$ is cyclic.

A supersolvable group is solvable.

Finitely generated nilpotent groups are supersolvable.

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