Kummer’s lemma and picard groups of integer group rings

الملخص EN

In this paper we re-prove a result by Kervaire and Murthy concerning Picard groups of integer group rings ZC, where C is a cyclic group of prime power order.

Our method is more elementary than the one used by Kervaire and Murthy and relies on the construction of certain multiplicative maps by Stolin and on a generalization of Kummer’s Lemma on units in cyclotomic fields presented here.