University of Guilan Journal of Algebra and Related Topics 2345-3931 9 1 2021 06 01 Nearrings of functions without identity determined by a single subgroup 121 129 4813 10.22124/jart.2021.15730.1190 EN G. Alan Cannon Department of Mathematics, Southeastern Louisiana University, SLU 10687 Hammond, LA 70402, USA V. Enlow Department of Mathematics, Southeastern Louisiana University Hammond, LA 70402, USA Journal Article 2020 02 15 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 $M = \{f : G \to G\ |\ f(G) \subseteq H \ \hbox{and}\ f(0) = 0 \}$ 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 $M$. https://jart.guilan.ac.ir/article_4813_288624afb20502195541c69de3b63864.pdf