HIGHER CLASS GROUPS OF GENERALIZED EICHLER ORDERS.

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