Skip to main content
Log in

Two-Transitive Parallelisms

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

In this article, the parallelisms whichadmit doubly transitive groups are completely classified as thetwo regular parallelisms in \(PG\left( {3,2} \right)\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. J. André, Über Perspektivitaten in endliche projektiven Ebenen, Arch. Math., Vol. 6 (1954), pp. 26–32.

    Google Scholar 

  2. P. Ribenboim, Catalan's Conjecture, Academic Press, Boston (1994).

    Google Scholar 

  3. R.H.F. Denniston, Packings of PG(3,q), Finite Geometric Structures and their Applications, Bressanone (1972) Cremonese (1973) pp. 195–199.

  4. R.H.F. Denniston, Cyclic packings of projective spaces, Atti Accad. Naz. Lincei, Vol. 8 (1972), pp. 36–40.

    Google Scholar 

  5. M.E. Harris and Ch. Hering, On the smallest degrees of projective representations of the groups PSL(n, q), Canad. J. Math., Vol. 23 (1971) pp. 90–102.

    Google Scholar 

  6. D.A. Foulser, Subplanes of partial spreads in translation planes, Bull. London Math. Soc., Vol. 4 (1972) pp. 1–7.

    Google Scholar 

  7. D.A. Foulser, Baer p-elements in translation planes, J. Alg., Vol. 86 (1974), pp. 354–366.

    Google Scholar 

  8. D.A. Foulser and N.L. Johnson, The translation planes of order q 2 that admit SL(2,q), I. Even Order, J. Alg., Vol. 82 (1984) pp. 385–406.

    Google Scholar 

  9. Ch. Hering, On shears of translation planes, Abh. Math. Sem. Univ. Hamburg, Vol. 37 (1972) pp. 258-268.

    Google Scholar 

  10. Ch. Hering, On projective planes of type VI, Atti Convegni Lincei, Vol. 17; Teor. Combinatorie II (1976) pp. 29–53.

    Google Scholar 

  11. M.J. Ganley, Baer involutions in semifields of even order, Geom. Ded., Vol. 2 (1973) pp. 499–508.

    Google Scholar 

  12. M. Ganley, V. Jha and N.L. Johnson, The translation planes admitting a nonsolvable doubly transitive linesized orbit, J. Geom. (to appear).

  13. V. Jha and N.L. Johnson, Regular parallelisms from translation planes, Discrete J. Math., Vol. 59 (1986) pp. 91–97.

    Google Scholar 

  14. V. Jha and N.L. Johnson, Coexistence of elations and large Baer groups in translation planes, J. London Math. Soc., Vol. 32 (1985) pp. 297–304.

    Google Scholar 

  15. V. Jha and N.L. Johnson, Baer involutions in translation planes admitting large elation groups, Results in Math., Vol. 11 (1987) pp. 63–71.

    Google Scholar 

  16. N.L. Johnson, The maximal special linear groups that act on translation planes, Boll. U.M.I., Vol. 6 (1986) pp. 349–352.

    Google Scholar 

  17. N.L. Johnson and T.G. Ostrom, Tangentially transitive planes of order 16, J. Geom., Vol. 10 (1977) pp. 146–163.

    Google Scholar 

  18. N.L. Johnson and T.G. Ostrom, The translation planes of order 16 which admit PSL(2,7), J. Comb. Theory (Series A), Vol. 26 (1979) pp. 127–l34.

    Google Scholar 

  19. M.J. Kallaher and T.G. Ostrom, Fixed point free linear groups, rank three planes, and Bol-quasifields, J. Alg., Vol. 18 (1989) pp. 50–73.

    Google Scholar 

  20. W.M. Kantor, Homogeneous designs and geometric lattices, J. Comb. Theory (Series A), Vol. 38 (1985) pp. 66–74.

    Google Scholar 

  21. W. Ljunggren, Einige Bemerkungen über die Darstellung ganzer Zahlen durch binäre kubische Former mit positiver Diskriminante, Acta Math., Vol. 75 (1942) pp. 1–21.

    Google Scholar 

  22. T.G. Ostrom, Linear transformations and collineations of translation planes, J. Alg.,Vol. 3 (1970) pp. 405–416.

    Google Scholar 

  23. T. Penttila and B. Williams, Regular packings in PG(3,q), European Journal of Combinatorics, Vol. 19 (1998) pp. 713–720.

    Google Scholar 

  24. A. Prince, The cyclic parallelisms of PG(3, 5), European J. Combin., Vol. 19 (1998) pp. 613–616.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Johnson, N.L. Two-Transitive Parallelisms. Designs, Codes and Cryptography 22, 179–189 (2001). https://doi.org/10.1023/A:1008321206709

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008321206709

Keywords

Navigation