Definition. A sequence (G0,G1, …,Gr) of subgroups of a group G is called a normal series (or subnormal series,) of G if
The factors of a normal series are the quotient groups Gi /Gi–1, 1 ≤ i ≤ r.
Definition. A composition series of a group G is a normal series (G0, …,Gr) without repetition whose factors Gi/Gi-1 are all simple groups. The factors Gi/Gi-1 are called composition factors of G.
We often refer to a normal series (G0, G1, …,Gr) by saying that
is a normal series of G.
For any group is trivially ...