Symplectic spreads in PG(3, q), inversive planes and projective planes

Discrete Mathematics

Volumn 174, Issue 1-3, 1997, Pages 329-336

  Thas, J A ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4644311644     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(96)00345-7     Document Type: Article

References (38)

1. A. Barlotti, Un' estensione del teorema di Segre-Kustaanheimo, Boll. Un. Mat. Ital. 10 (1955) 96-98.
2. A. Beutelspacher, Projective planes, in: F. Buekenhout, ed., Handbook of Incidence Geometry, Ch. 4 (North-Holland, Amsterdam, 1995) 107-136.
3. A. Blokhuis and G.E. Moorhouse, Some p-ranks related to orthogonal spaces, J. Alg. Combin. 14 (1995) 295-316.
4. R.H. Bruck, Construction problems of finite projective planes, in: Combinatorial Mathematics and its Applications, University of North Carolina, 1967 (University of North Carolina Press, North Carolina, 1969) 426-514.
5. T. Czerwinski, The collineation groups of the translation planes of order 25, Geom. Dedicate 39 (1991) 125-137.
6. T. Czerwinski and D. Oakden, The translation planes of order twenty-five, J. Combin. Theory Ser. A 59 (1992) 193-217.
7. E.H. Davis, Translation planes of order 25 with non-trivial X -OY perspectivities, Congr. Numer. (1979) 23-24, 341-348.
8. P. Dembowski, Inversive planes of even order, Bull. Amer. Math. Soc. 69 (1963) 850-854.
9. P. Dembowski, Finite Geometries (Springer, Berlin, 1968).
10. G. Fellegara, Gli ovaloidi di uno spazio tridimensionale di Galois di ordine 8, Atti Accad. Naz. Lincei Rend. 32 (1962) 170-176.
11. D.G. Glynn, The Hering classification for inversive planes of even order, Simon Stevin 58 (1984) 319-353.
12. J.W.P. Hirschfeld, Finite Projective Spaces of Three Dimensions (Oxford University Press, Oxford, 1985).
13. J.W.P. Hirschfeld and J.A. Thas, General Galois Geometries (Oxford University Press, Oxford, 1991).
14. W.M. Kantor, Ovoids and translation planes, Canad. J. Math. 34 (1982) 1195-1207.
15. G. Lunardon, 1993, private communication.
16. R. Mathon and G.F. Royle, Translation planes of order 49, Des. Codes Cryptogr. 5 (1995) 57-72.
17. D.J. Oakden, Spreads in Three-dimensional Projective Space, Ph.D. Thesis, University of Toronto, 1973.
18. C.M. O'Keefe and T. Penttila, Ovoids of PG(3, 16) are elliptic quadrics, J. Geom. 38 (1990) 95-106.
19. C.M. O'Keefe and T. Penttila, Ovoids of PG(3, 16) are elliptic quadrics, II, J. Geom. 44 (1992) 140-159.
20. C.M. O'Keefe and J.A. Thas, Ovoids of the quadric Q(2n, q), n>2, European J. Combin. 16 (1995) 87-92.
21. C.M. O'Keefe, T. Penttila and G.F. Royle, Classification of ovoids in PG(3,32), J. Geom. 50 (1994) 143-150.
22. G. Panella, Caratterrizzazione delle quadriche di uno spazio (tridimensionale) lineare sopra un corpo finite, Boll. Un. Mat. Ital. 10 (1955) 507-513.
23. N.J. Patterson, A four-dimensional Kerdock set over GF(2), J. Combin. Theory Ser. A 20 (1976) 365-366.
24. T. Penttila and C.E. Praeger, Ovoids and translation ovals, London Math. Soc., to appear.
25. O. Prohaska and M. Walker, A note on the Hering type of inversive planes of even order, Arch. Math. 28 (1977) 431-432.
26. +(10, 3), J. Combin. Theory Ser. A 51 (1989) 250-257.
27. L. Storme and J.A. Thas, k-arcs and partial flocks, Linear Algebra Appl. 226-228 (1995) 33-45.
28. J.A. Thas, Ovoidal translation planes, Arch. Math. 23 (1972) 110-112.
29. J.A. Thas, Flocks of finite egglike inversive planes, in: Finite Geometric Structures and their Applications, Bressanone, 1972 (Cremonese, Roma, 1973) 189-191.
30. J.A. Thas, Flocks of nonsingular ruled quadrics in PG(3, q), Atti Accad. Naz. Lincei Rend. 59 (1975) 83-85.
31. J.A. Thas, Ovoids and spreads of finite classical polar spaces, Geom. Dedicata 10 (1981) 135-144.
32. J.A. Thas, Generalized quadrangles and flocks of cones, European. J. Combin. 8 (1987) 441-452.
33. J.A. Thas, Old and new results on spreads and ovoids of finite classical polar spaces, in: Combinatorics '90, Ann. Discrete Math. 52 (1992) 529-544.
34. J.A. Thas, 1993, unpublished notes.
35. J.A. Thas, The affine plane AG(2, q), q odd, has a unique one point extension, Invent. Math. 118 (1994) 133-139.
36. J.A. Thas, Projective geometry over a finite field and generalized polygons, in: F. Buekenhout, ed., Handbook of Incidence Geometry, Chs. 7 and 9 (North-Holland, Amsterdam, 1995) 295-348 and 383-432.
37. J.A. Thas and S.E. Payne, Spreads and ovoids in finite generalized quadrangles, Geom. Dedicata 52 (1994) 227-253.
38. J. Tits, Ovoïdes et groupes de Suzuki, Arch. Math. 13 (1962) 187-198.