nLab Jordan-Hölder theorem


The Jordan-Hölder theorem says that every composition series of a given group, and every Jordan-Hölder sequence on a given object in an abelian category, has the same length, and the same simple factors, up to permutation. In particular says that the length of an object in an abelian category is well defined.

More generally, a form of the theorem holds in any homological category.


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