A construction of monogenic near-ring groups, and some applications

Abstract

Let V be a group generated by elements ν1 and ν2 of finite coprime order, and let N be the near-ring generated by the inner automorphism induced by ν1.It is proved that V is a monogenic N-group. Certain consequences of this result are discussed. There exist finite near-rings N with identity generated by a single distributive element μ, such that μ2 = 1 and where the radical J2(N) (see Günter Pilz, Near-rings. The theory and its applications, 1977, p. 136) is non-nilpotent.