Ordered Generating Systems of Finite Non-Abelian Groups

Abstract

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.