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

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 from a principal and arbitrary characters , and Artin exponent(a(G)) of [] cyclic subgroups from arbitrary characters .