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

Published online by Cambridge University Press:  17 April 2009

S.D. Scott
S.D. Scott
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 1 , August 1978 , pp. 1 - 4
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Pilz, Günter, Near-rings. The theory and its applications (North-Holland Mathematics Studies, 23. North-Holland, Amsterdam, New York, Oxford, 1977).Google Scholar
[2]Schenkman, Eugene, Group theory (Van Nostrand, Princeton, New Jersey; Toronto; New York; London; 1965).Google Scholar