Class groups of cyclic groups of square-free order

Abstract

Let G G be a finite cyclic group of square free order. Let Cl( Z G ) {\text {Cl(}}ZG{\text {)}} denote the projective class group of the integral group ring Z G ZG . Our main theorem describes explicitly the quotients of a certain filtration of Cl( Z G ) {\text {Cl(}}ZG{\text {)}} . The description is in terms of class groups and unit groups of the rings of cyclotomic integers involved in Z G ZG . The proof is based on a Mayer-Vietoris sequence.