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.
Butzman, S., Cannon, G., & Paz, M. (2022). Centers of centralizer nearrings determined by All endomorphisms of symmetric groups. Journal of Algebra and Related Topics, 10(2), 13-26. doi: 10.22124/jart.2022.21398.1357
MLA
S. Butzman; G. A. Cannon; M. A Paz. "Centers of centralizer nearrings determined by All endomorphisms of symmetric groups". Journal of Algebra and Related Topics, 10, 2, 2022, 13-26. doi: 10.22124/jart.2022.21398.1357
HARVARD
Butzman, S., Cannon, G., Paz, M. (2022). 'Centers of centralizer nearrings determined by All endomorphisms of symmetric groups', Journal of Algebra and Related Topics, 10(2), pp. 13-26. doi: 10.22124/jart.2022.21398.1357
VANCOUVER
Butzman, S., Cannon, G., Paz, M. Centers of centralizer nearrings determined by All endomorphisms of symmetric groups. Journal of Algebra and Related Topics, 2022; 10(2): 13-26. doi: 10.22124/jart.2022.21398.1357
)