A theorem in group theory
, this states that the composition factor
s of a group
are unique, up to the order you write them in.
In more technical terms, if G is a group
is a composition series
for G, then the composition factor
are unique to within rearrangement.
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.