On the centralizers of monoids in clone theory

For a set S of functions of k-valued logic, the centralizer S* is the set of functions which ´permute´ with all functions in S. As a continuation of our previous work we study the centralizers for certain monoids consisting of unary functions. First we show that the centralizers of permutation groups are distinct to each other, and then characterize the centralizer of the alternating group. Next, for certain monoids whose centralizer is the smallest clone J_k, we study the centralizers of some of its proper submonoids. In particular, we report the existence of a considerably small monoid whose centralizer is J_k as well.