ACTA ARITHMETICA

On the l-divisibility of the relative class number of certain cyclic number fields by Kurt Girstmair (Innsbruck) Introduction. Let q be a natural number and p a prime with 2q | p − 1. Let ξp = e2pii/p and Qp = Q(ξp), i.e., the pth cyclotomic field. Moreover, consider Fp = Z/pZ = {0, 1,..., p − 1} and the multiplicative group Gp = F×p of this field. There is a canonical group isomorphism Gp → Gal(Qp/Q) : k 7 → σk