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G is called an Artin exponent for G (see [5]). All Artin exponents form an ideal in the integers and clearly |G| is in this ideal. The unique positive generator for this ideal is called the Artin exponent of G. Now let G(QG) denote the Grothendieck ring of all rational representations of G and GC(QG) the ideal in G(QG) generated by rational representations of G induced from cyclic subgroups. The Artin exponent of G has been computed by finding the characteristic of the quotient ring G(QG)/GC(QG) (see [5]). The purpose of this paper is to compute the same invariant (the Artin

Certain applications of the Burnside rings and ghost rings in the representation theory of finite groups. I.