Main Page | See live article | Alphabetical index 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. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.