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Translation complements of C-planes: (I)

  • M. L. Narayana Rao (a1), K. Kuppuswamy Rao (a2) and G. V. Subba Rao (a1)
Abstract

Narayana Rao, Rodabaugh, Wilke and Zemmer constructed a new class of finite translation planes from exceptional near-fields described by Dickson and Zassenhaus. These planes referred to as C-planes are not coordinatized by the generalized André systems. In this paper we compute the translation complement of the C-plane corresponding to the C-system III–1. It is found that the translation complement is of order 6912 and it divides the set of ideal points into two orbits of lengths 2 and 48.

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Copyright
COPYRIGHT: © Australian Mathematical Society 1987
References
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[1]André, J., “Uber nicht-Desarguessche Ebenen mit transitiver translation gruppe”, Math. Z. 60 (1954), 156–186.
[2]Dembowski, P., Finite Geometries, (Springer-Verlag, 1968).
[3]Hall, Marshall Jr., The Theory of Groups (Macmillan 1959).
[4]Lueder, Kenneth, “Derivability in the irregular nearfield planes”,Proceedings of the International Conference on Projective planes, (Washington State University Press 1973), 181–189.
[5]Narayana Rao, M.L. and Davis, E.H., “Construction of Translation Planes from t-spread sets”, J. Combinatorial Theory Ser. A. 14, (1973) 201–208.
[6]Narayana Rao, M.L.Rodabaugh, D.J., Wilke, F.W. and Zemmer, J.L., “A new class of finite translation planes obtained from the exceptional nearfields”, J. Combinatorial Theory Ser. A. 11 (1971), 72–92.
[7]Narayana Rao, M.L. and Satyanarayana, K., “A new class of square order planes”, J. Combinatorial Theory Ser. A. 35 (1983), 33–42.
[8]Narayana Rao, M.L. and Satyanarayana, K., “On a C-plane of order 25”, Bull. Austral. Math. Soc. 30, (1984), 27–36.
[9]Ostrom, T.G., “Classifications of finite translation planes”,Proceedings International Conference on Projective planes, (Washington State University Press 1973), 195–213.
[10]Pickert, G., Projective Ebenen, (Springer Verlag, 1955).
[11]Walker, M., “A class of translation planes”, Geom. Dedicata, 5, (1976), 135–146.
[12]Zassenhaus, H., “Uber endlicher Fastkörper”, Abh. Math. Sem. Univ. Hamburg, 11 (1936), 187–220.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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