@article {Beidar:1 November 1996:0021-8693:688, author = "Beidar, K.", author = "Fong, Y.", author = "Ke, W.F.", title = "On Finite Circular Planar Nearrings", journal = "Journal of Algebra", volume = "185", year = "1 November 1996", 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.", pages = "688-709(22)", url = "http://www.ingentaconnect.com/content/ap/ja/1996/00000185/00000003/art00347" }