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.

- David Speyer,
*The Jordan-Hölder theorem*(pdf)

Last revised on January 10, 2020 at 15:28:14. See the history of this page for a list of all contributions to it.