A class number formula for elementary-abelian-group rings

AbstractLet G be an elementary abelian group of order lk, where l is an odd prime. The order of the “odd part” of the class group Cl(ZG) of the integral group ring ZG is shown to be the “odd part” of the index of a Stickelberger ideal in the group ring ZC, where C≌(Flk)x. Analogous results are obtained for elementary abelian 2-groups. For k = 1, this coincides with Iwasawa's class number formula for the cyclotomic field Q(μl). The Stickelberger ideal is a relative of one introduced by Kubert and Lang based on a Cartan subgroup C(N) of C(N)ofGl2(ZN)