Jordan-Hölder decomposition

A Jordan–Hölder decomposition of a group $G$ is a filtration

$$G=G_1\supset G_2\supset \mathrm{\cdots }\supset G_n=\{1\}$$

such that $G_{i+1}$ is a normal subgroup of $G_i$ and the quotient $G_i/G_{i+1}$ is a simple group for each $i$.

Title	Jordan-Hölder decomposition
Canonical name	JordanHolderDecomposition
Date of creation	2013-03-22 12:08:41
Last modified on	2013-03-22 12:08:41
Owner	djao (24)
Last modified by	djao (24)
Numerical id	9
Author	djao (24)
Entry type	Definition
Classification	msc 20E15
Synonym	composition series
Related topic	DerivedSubgroup
Related topic	JordanHolderDecompositionTheorem