Ramsey Varieties of Finite Groups

Let :Yt be a class of finite algebras closed under the operations of taking quotients, subalgebras andfinite direct products. For any algebras D and E in :Yt let (g) denote the set ofsubalgebras ofE isomorphic to D. For what A, Bin :Yt and r a natural number does there exist a C in:Yt such that for any partition of(~) into r classes there exists a member jj of(~) such that (1) is contained in one of the classes?