The Relation Among A(G), M(G) ,M'(G )& a(G)

Abstract

The main object of this paper is to find the relation among definitions of Artin exponent (A(G) ,M(G) ,M'(G) ) of cyclic subgroups from a principal characters ,and Artin exponent of the subgroups G [σ] from a principal and arbitrary characters , and Artin exponent(a(G)) of cyclic subgroups from arbitrary characters.