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:GG | f(G)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