A theorem in group theory, this states that the composition factors of a group are unique, up to the order you write them in. In more technical terms, if G is a group and G=G1>G2>...>Gn>Gn+1={1} is a composition series for G, then the composition factors Gi/Gi+1 are unique to within rearrangement.

ie. if
is another composition series for G, then n=k and there is a permutation f in Sn such that Gi/Gi+1 is isomorphic to Hf(i)/Hf(i)+1.

The proof of the Jordan-Hölder theorem is by induction on the size of the group, and is an application of the second and third isomophism theorems.

Log in or register to write something here or to contact authors.