Centers of centralizer nearrings determined by inner automorphisms of symmetric groups

The question of identifying the elements of the center of a nearring and of determining when that center is a subnearring is an area of continued research. We consider the centers of centralizer nearrings, MI(Sn), determined by the symmetric groups Sn with n≥3 and the inner automorphisms I=Inn Sn. General tools for determining elements of the center of MI(Sn) are developed, and we use these to list the specific elements in the centers of MI(S4), MI(S5), and MI(S6).