example of a Jordan-Hölder decomposition

A group that has a composition seriesMathworldPlanetmathPlanetmath will often have several different composition series.

For example, the cyclic groupMathworldPlanetmath C12 has (E,C2,C6,C12), and (E,C2,C4,C12), and (E,C3,C6,C12) as different composition series. However, the result of the Jordan-Hölder Theorem is that any two composition series of a group are equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath, in the sense that the sequence of factor groups in each series are the same, up to rearrangement of their order in the sequence Ai+1/Ai. In the above example, the factor groups are isomorphicPlanetmathPlanetmathPlanetmath to (C2,C3,C2), (C2,C2,C3), and (C3,C2,C2), respectively.

This is taken from the http://en.wikipedia.org/wiki/Solvable_groupWikipedia article on solvable groupsMathworldPlanetmath.

Title example of a Jordan-Hölder decomposition
Canonical name ExampleOfAJordanHolderDecomposition
Date of creation 2013-03-22 14:24:33
Last modified on 2013-03-22 14:24:33
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 10
Author mathcam (2727)
Entry type Example
Classification msc 20E15
Synonym example of Jordan-Holder decomposition