# 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.

Title supersolvable group SupersolvableGroup 2013-03-22 13:58:44 2013-03-22 13:58:44 mclase (549) mclase (549) 5 mclase (549) Definition msc 20F16 msc 20D10 PolycyclicGroup supersolvable