Higher class groups of generalized Eichler orders

摘要

In this paper we study the possible torsion in even-dimensional higher class groups Cl-2n (Lambda) (n >= 1) of an order Lambda in a semisimple algebra A over a number field F with a ring of integers O-F. We show that for certain orders, called generalized Eichler orders, p-torsion in Cl-2n (Lambda) can only occur for primes p dividing prime ideals p of O-F, at which A is not maximal. In particular, the results apply to Eichler orders in quaternion algebras and to hereditary orders.