Simplicity of Full Centralizer Nearrings and Exponent-Preserving Groups

Neuerburg, Kent; Cannon, G. Alan; Walls, Gary

doi:10.30504/jims.2026.485189.1215

Simplicity of Full Centralizer Nearrings and Exponent-Preserving Groups

Articles in Press

Document Type : Research Article

Authors

Kent Neuerburg ¹

G. Alan Cannon ²

Gary Walls ¹

¹ Department of Mathematics Southeastern Louisiana University Hammond, LA USA

² Department of Mathematics Southeastern Louisiana University'Hammond, LA USA

10.30504/jims.2026.485189.1215

Abstract

The simplicity of $M_S(G)$, the centralizer nearring determined by a finite group $G$ and a semigroup $S$ of endomorphisms of $G$, is determined for the cases of $S = \Inn G$ and $S = \Aut G$. The concept of exponent-preserving (EP) groups is defined and is used to study the simplicity of $M_E(G)$ where $E = \End G$ and $G$ has a cyclic Sylow $p$-subgroup.

Keywords

centralizer nearring

simplicity

exponent

Sylow $p$-subgroup

Subjects