Centers of centralizer nearrings determined by inner automorphisms of symmetric groups

Abstract

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 $n geq 3$ 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 $M_I(S_4)$, $M_I(S_5)$, and $M_I(S_6)$.