Units in regular elementary abelian group rings

Abstract

If P is a regular prime and A an elementary abelian p-group, every unit in the integral group ring of A is a product of units coming from cyclic subgroups of A. If P is irregular, there is always a shortfall described by a finite abelian p-group. The shape of the latter depends on a con­ jecture about global versus local cyclotomic units which has been verified for p < 10,000.