ON FINITE CIRCULAR PLANAR NEARRINGS

The main subject of this paper is to characterize finite circular Ferr ero 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, Oxf ord Univ. Press, Oxford, 1992) is presented for finite circular Ferrer o pairs (N, Phi) with cyclic Phi. We show that the fixed point free gr oup of automorphisms Phi of a finite circular Ferrero pair (N, Phi) is metacyclic. Finally, two questions on the existence of nonabelian cir cular planar nearrings are answered by a general construction method a nd some basic examples. (C) 1996 Academic Press, Inc.