Nearrings of functions without identity determined by a single subgroup

Document Type : Research Paper

Authors

¹ Department of Mathematics, Southeastern Louisiana University, SLU 10687 Hammond, LA 70402, USA

² Department of Mathematics, Southeastern Louisiana University Hammond, LA 70402, USA

Abstract

Let

(G, +)

be a finite group, written additively with identity 0, but not necessarily abelian, and let

H

be a nonzero, proper subgroup of

G

. Then the set

M = {f : G \to G | f (G) \subseteq H and f (0) = 0}

is a right, zero-symmetric nearring under pointwise addition and function composition. We find necessary and sufficient conditions for

M

to be a ring and determine all ideals of

M

, the center of

M

, and the distributive elements of

M

Keywords