On Finite Circular Planar Nearrings

Authors: Beidar, K.1; Fong, Y.1; Ke, W.F.1

Source: Journal of Algebra, Volume 185, Number 3, 1 November 1996 , pp. 688-709(22)

Publisher: Academic Press

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Abstract:

The main subject of this paper is to characterize finite circular Ferrero pairs, the tool for constructing finite circular planar nearrings. A general characterization of finite circular Ferrero pairs is given. In particular, a generalized version of Modisett's characterization (see J. R. Clay "Nearrings: Geneses and Applications," pp. 68-75, Oxford Univ. Press, Oxford, 1992) is presented for finite circular Ferrero pairs ( N , Phi) with cyclic Phi. We show that the fixed point free group of automorphisms Phi of a finite circular Ferrero pair ( N , Phi) is metacyclic. Finally, two questions on the existence of nonabelian circular planar nearrings are answered by a general construction method and some basic examples.

Document Type: Research article

Affiliations: 1: Department of Mathematics, National Cheng Kung University, Tainan, 701, Taiwan, Republic of China

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