example of a Jordan-Hölder decomposition
A group that has a composition series will often have several different composition series.
For example, the cyclic group has , and , and as different composition series. However, the result of the Jordan-Hölder Theorem is that any two composition series of a group are equivalent, in the sense that the sequence of factor groups in each series are the same, up to rearrangement of their order in the sequence . In the above example, the factor groups are isomorphic to , , and , respectively.
This is taken from the http://en.wikipedia.org/wiki/Solvable_groupWikipedia article on solvable groups.
|Title||example of a Jordan-Hölder decomposition|
|Date of creation||2013-03-22 14:24:33|
|Last modified on||2013-03-22 14:24:33|
|Last modified by||mathcam (2727)|
|Synonym||example of Jordan-Holder decomposition|