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,Φ) with cyclic Φ. We show that the fixed point free group of automorphisms Φ of a finite circular Ferrero pair (N,Φ) is metacyclic. Finally, two questions on the existence of nonabelian circular planar nearrings are answered by a general construction method and some basic examples.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory