The two-prime analogue of the Hecke C*-algebra of Bost and Connes

Let p and q be distinct odd primes. We analyse a semigroup crossed product C * (G p,q) α 2 similar to the semigroup crossed product which models the Hecke C * -algebra of Bost and Connes. We describe a composition series of ideals in C * (G p,q) α 2 , and show that the structure of one of the subquotients reflects interesting number-theoretic information about the multiplicative orders of q in the rings Z/pl Z.