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A construction of monogenic near-ring groups, and some applications
Published online by Cambridge University Press: 17 April 2009
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.
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- Copyright © Australian Mathematical Society 1979
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