solvable group

A group $G$ is solvable if it has a subnormal series

$$G=G_0\supset G_1\supset \mathrm{\cdots }\supset G_n=\{1\}$$

where all the quotient groups $G_i/G_{i+1}$ are abelian.

Title	solvable group
Canonical name	SolvableGroup
Date of creation	2013-03-22 12:08:53
Last modified on	2013-03-22 12:08:53
Owner	djao (24)
Last modified by	djao (24)
Numerical id	11
Author	djao (24)
Entry type	Definition
Classification	msc 20A05
Synonym	solvable
Synonym	soluble group
Related topic	DerivedSubgroup
Related topic	CompositionSeries2
Related topic	GaloisCriterionForSolvabilityOfAPolynomialByRadicals