  In this paper we define Ordered Generating System for finite non-abelian
groups, which is a generalization of the basis theorem for finite abelian
groups. We prove the following: If each composition factor of a group G has
Ordered Generating System, then G has Ordered Generating System as well. Hence,
it remains to prove that every finite simple group has Ordered Generating
System. In this paper we prove that the sporadic group of Mathieu has the
property of Ordered Generating System.
