NEARRINGS OF FUNCTIONS WITHOUT IDENTITY DETERMINED BY A SINGLE SUBGROUP

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 → g | 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.