Jordan-Hölder decomposition theorem

Every finite groupMathworldPlanetmath G has a filtrationPlanetmathPlanetmath


where each Gi+1 is normal in Gi and each quotient groupMathworldPlanetmath Gi/Gi+1 is a simple groupMathworldPlanetmathPlanetmath. Any two such decompositions of G have the same multiset of simple groups Gi/Gi+1 up to ordering.

A filtration of G satisfying the properties above is called a Jordan–Hölder decomposition of G.

Title Jordan-Hölder decomposition theorem
Canonical name JordanHolderDecompositionTheorem
Date of creation 2013-03-22 12:08:44
Last modified on 2013-03-22 12:08:44
Owner djao (24)
Last modified by djao (24)
Numerical id 9
Author djao (24)
Entry type Theorem
Classification msc 20E32
Related topic SubnormalSeries
Defines Jordan-Hölder decomposition