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Applications of line geometry over finite fields II. The Hermitian surface

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Bibliography

  1. Baker, H.F., Principles of Geometry, Vol. III, Cambridge, 1923 (Ungar, 1961).

  2. Barth, W., ‘Submanifolds of Low Codimension in Projective Space’, Proc. Int. Cong. of Mathematicians (Vancouver, 1974), Canadian Mathematical Congress, 1975.

  3. Bose, R.C. and Chakravarti, I.M., ‘Hermitian Varieties in a Finite Projective Space PG(N, q 2)’, Can. J. Math. 19, 1161–1182 (1966).

    Google Scholar 

  4. Bruen, A.A. and Hirschfeld, J.W.P., ‘Applications of Line Geometry over Finite Fields. I. The Twisted Cubic’, Geometriae Dedicata 6, 495–509 (1977).

    Google Scholar 

  5. Bruen, A.A. and Thas, J.A., ‘Partial Spreads, Packings and Hermitian Manifolds in PG(3, q)’, Math. Z. 151, 207–214 (1976).

    Google Scholar 

  6. Buekenhout, F. and Lefèvre, C., ‘Generalized Quadrangles in Projective Spaces’, Arch. Math. 25, 540–552 (1974).

    Google Scholar 

  7. Coxeter, H.S.M., ‘Self-Dual Configurations and Regular Graphs’, Bull. Am. Math. Soc. 56, 413–455 (1950).

    Google Scholar 

  8. Dieudonné, J., La géométrie des groupes classiques (2nd edn), Springer, 1963.

  9. Edge, W.L., ‘The Isomorphism between LF(2, 32) and A 6’, J. London Math. Soc. 30, 172–185 (1955).

    Google Scholar 

  10. Edge, W.L., ‘Quadrics over GF(2) and their Relevance for the Cubic Surface Group’, Can. J. Math. 11, 625–645 (1959).

    Google Scholar 

  11. Edge, W.L., ‘Some Implications of the Geometry of the 21-Point Plane’, Math. Z. 87, 348–362 (1965).

    Google Scholar 

  12. Gewirtz, A., ‘Graphs with Maximal Even Girth’, Can. J. Math. 21, 915–934 (1969).

    Google Scholar 

  13. Gewirtz, A., ‘The Uniqueness of G(2, 2, 10, 56)’, Trans. New York Acad. Sci. 31, 656–675 (1969).

    Google Scholar 

  14. Goethals, J.M. and Seidel, J.J., ‘Strongly Regular Graphs and Combinatorial Designs’, Can. J. Math. 22, 597–614 (1970).

    Google Scholar 

  15. Hall, M., Lane, R. and Wales, D., ‘Designs Derived from Permutation Groups’, J. Comb. Theory 8, 12–22 (1970).

    Google Scholar 

  16. Hill, R., ‘On the Largest Size of Cap in S 5,3’, Atti Accad. Naz. Lincei Rend. 54, 378–384 (1973).

    Google Scholar 

  17. Hill, R., ‘Caps and Codes’ (to appear).

  18. Hirschfeld, J.W.P., ‘The Double-six of Lines over PG(3, 4)’, J. Austral. Math. Soc. 4, 83–89 (1964).

    Google Scholar 

  19. Hirschfeld, J.W.P., ‘Classical Configurations over Finite Fields: I. The Double-Six and the Cubic Surface with 27 Lines’, Rend. Mat. Appl. 26, 115–152 (1967).

    Google Scholar 

  20. Hirschfeld, J.W.P., ‘Classical Configurations over Finite Fields: II. Grace's Extension of the Double-Six’, Rend. Mat. Appl. 26, 349–374 (1967).

    Google Scholar 

  21. Hirschfeld, J.W.P., ‘A Configuration of Lines in Three Dimensions’ Proc. Edinb. Math. Soc. 19, 105–123 (1972).

    Google Scholar 

  22. Hirschfeld, J.W.P., Projective Geometries over Finite Fields Oxford (to appear).

  23. Hubaut, X.L., ‘Strongly Regular Graphs’, Discrete Math. 13, 357–381 (1975).

    Google Scholar 

  24. Jessop, C.M., A Treatise on the Line Complex, Cambridge, 1903 (Chelsea, 1969).

  25. Jónsson, W., ‘The (56, 11, 2) Design of Hall, Lane, and Wales’, J. Comb. Theory (A) 14, 113–118 (1973).

    Google Scholar 

  26. Longuet-Higgins, M.S., ‘Clifford's Chain and its Analogues in Relation to the Higher Polytopes’, Proc. Roy. Soc. London A330, 443–466 (1972).

    Google Scholar 

  27. Montague, S., ‘On Rank 3 Groups with a Multiply Transitive Constituent’, J. Algebra 13, 506–522 (1970).

    Google Scholar 

  28. Pellegrino, G., ‘Sul massimo ordine delle calotte in S 4,3’, Matematiche 25, 149–157 (1970).

    Google Scholar 

  29. Segre, B., ‘Forme e geometrie hermitiane, con particolare riguardo al caso finito’, Ann Mat. Pura Appl. 70, 1–202 (1965).

    Google Scholar 

  30. Segre, B., ‘Introduction to Galois Geometries’, Atti Accad. Naz. Lincei Mem. 8, 133–236 (1967).

    Google Scholar 

  31. Tallini Scafati, M., ‘Caratterizzazione grafica delle forme hermitiane di un S r,q’, Rend. Mat. Appl. 26, 273–303 (1967).

    Google Scholar 

  32. van der Waerden, B.L., Gruppen von linearen Transformationen, Springer, 1935 (Chelsea, 1948).

  33. Wales, D., ‘Uniqueness of the Graph of a Rank 3 Group’, Pacific J. Math. 30, 271–277 (1969).

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Mathematics, University of Western Ontario, N6A 3K7, London, Canada

    A. A. Bruen

  2. Mathematics Division, University of Sussex, BN1 9QH, Brighton, United Kingdom

    J. W. P. Hirschfeld

Authors
  1. A. A. Bruen
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  2. J. W. P. Hirschfeld
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This work was partially supported by the National Research Council of Canada.

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Bruen, A.A., Hirschfeld, J.W.P. Applications of line geometry over finite fields II. The Hermitian surface. Geom Dedicata 7, 333–353 (1978). https://doi.org/10.1007/BF00151531

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  • DOI: https://doi.org/10.1007/BF00151531

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