Abstract
Czerwinski and Oakden have classified all the translation planes of order 25. In this paper the author gives the order and orbit lengths on the line at infinity of the collineation groups of these planes.
Similar content being viewed by others
References
André, J., ‘Über nicht-Desargessche Ebenen mit transitiver Translationsgruppe’, Math. Z. 60 (1954), 156–186.
Bruck, R. H., ‘Construction problems of finite projective planes’, Combinatorial Mathematics and its Applications (ed. R. C. Bose and T. A. Dowling), The University of North Carolina Press, Chapel Hill, North Carolina, 1969, pp. 426–514.
Czerwinski, R. T. and Oakden, D., ‘The translation planes of order twenty-five’ (submitted for publication).
Dembowski, P., Finite Geometries, Springer-Verlag, Berlin, 1968.
Dickson, L. E., ‘On finite algebras’, Nachr. Kgl. Ges. Wiss. Göttingen (1905), 358–393.
Foulser, D. A., ‘Solvable flag transitive affine groups’, Math. Z. 86 (1964), 191–204.
Hering, C., ‘A new class of quasifields’, Math. Z. 118 (1970), 56–57.
Oakden, D. J., ‘The regulus-containing spreads of PG(3,5), PhD Thesis, 1974, University of Toronto.
Oakden, D. J., ‘Methods for enumerating translation planes’, Private communication.
Orr, W. F., ‘The Miquelian inversive plane IP(q) and the associated projective planes’, PhD Thesis, 1973, University of Wisconsin.
Rao, M. L. N., Rodabaugh, D. J., Wilke, F. W., and Zemmer, J. L., ‘A new class of finite translation planes obtained from the exceptional near-fields’, J. Combin. Theory Ser. A 11 (1971), 72–92.
Rao, M. L. N. and Satyanarayana, K., ‘A new class of square order planes’, J. Combin. Theory Ser. A 35 (1983), 33–42.
Rao, M. L. N. and Satyanarayana, K., ‘On a c-plane of order 25’, Austral. Math. Soc. Bull. 30 (1984), 27–36.
Rao, M. L. N., ‘A translation of order 25’ (submitted for publication).
Veblen, O. and Young, J. W., Projective Geometry, Vol. I, Ginn, Boston, Mass., 1916.
Walker, M., ‘A class of translation planes’, Geom. Dedicata 5 (1976), 135–146.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Czerwinski, T. The collineation groups of the translation planes of order 25. Geom Dedicata 39, 125–137 (1991). https://doi.org/10.1007/BF00182289
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00182289