Centers of centralizer nearrings determined by All endomorphisms of symmetric groups

Document Type : Research Paper


1 Department of Mathematics, Southeastern Louisiana University, Hammond, United States

2 Department of Mathematics Southeastern Louisiana University Hammond, United States


For $n = 5, 6$ and $E = \End S_n$, the functions in the centralizer nearring $M_E(S_n) = \{f : S_n \to S_n \ |\ f(1) = (1) \ \hbox{and} \ f \circ s = s \circ f \ \hbox{for all}\ s \in E\}$ are determined.  The centers of these two nearrings are also described.  Results that can be used to determine the functions in $M_E(S_n)$ and their centers for $n \geq 7$ are also presented.