A

**composition series**of a group G is a chain of subgroups of G satisfying where stands for normal subgroup such that the quotient group of each link in the chain is a simple group.

For a finite group G, such a composition series certainly exists; and the isomorphism classes of simple groups are unique, up to permutation. This is called the **Jordan-Hölder theorem**.

See also Normal series.

*This article is a stub. You can help Wikipedia by fixing it.*