Some remarks on filtrations of hopf algebras

In this paper, the problem of nontrivial nearring multiplications on groups is closely investigated with a different approach. By using the notions of 5, 0-acts and the language of model theory, we give a detailed discussion on a large class of groups that possesses nontrivial nearring multiplications. In the last section, we apply our results to the theory of centralizer nearrings of a single endomorphism which is mainly due to the work of C. Maxson and K. Smith [28, 29]