supersolvable group

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

$$G=G_0⊳G_1⊳\mathrm{\cdots }⊳G_n=1$$

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
Canonical name	SupersolvableGroup
Date of creation	2013-03-22 13:58:44
Last modified on	2013-03-22 13:58:44
Owner	mclase (549)
Last modified by	mclase (549)
Numerical id	5
Author	mclase (549)
Entry type	Definition
Classification	msc 20F16
Classification	msc 20D10
Related topic	PolycyclicGroup
Defines	supersolvable