Given an arithmetic order in a semi-simple algebra A we consider higher class groups attached to the order.These groups are nite by a result of Kuku,and in an old result with Laubenbacher we showed that for odd higher class groups p-torsion is only possible if the localization of the order at a p-adic prime is not maximal.In a series of papers Guo and Kuku showed a similar result for the even class groups for certain families of orders.However,by a result of Guo,it is possible that an order has additonal p-torsion for primes p,which divide the dimension of the algebra A.In the talk we will survey the results and the techniques used.