Rings of congruence preserving functions

Let C0(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_0 (G)$$\end{document} denote the near-ring of congruence preserving functions of the group G. We investigate the question “When is C0(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_0 (G)$$\end{document} a ring?”. We obtain information externally via the lattice structure of the normal subgroups of G and internally via structural properties of the group G.