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, M_I(S_n), determined by the symmetric groups S_n with n \geq ۳ and the inner automorphisms I = Inn\ S_n.  General tools for determining elements of the center of M_I(S_n) are developed, and we use these to list the specific elements in the centers of M_I(S_۴), M_I(S_۵), and M_I(S_۶).

Keywords:

Centralizer nearring , center , inner automorphisms , Symmetric groups