Abstract
In this article, the parallelisms whichadmit doubly transitive groups are completely classified as thetwo regular parallelisms in \(PG\left( {3,2} \right)\).
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REFERENCES
J. André, Über Perspektivitaten in endliche projektiven Ebenen, Arch. Math., Vol. 6 (1954), pp. 26–32.
P. Ribenboim, Catalan's Conjecture, Academic Press, Boston (1994).
R.H.F. Denniston, Packings of PG(3,q), Finite Geometric Structures and their Applications, Bressanone (1972) Cremonese (1973) pp. 195–199.
R.H.F. Denniston, Cyclic packings of projective spaces, Atti Accad. Naz. Lincei, Vol. 8 (1972), pp. 36–40.
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.
D.A. Foulser, Subplanes of partial spreads in translation planes, Bull. London Math. Soc., Vol. 4 (1972) pp. 1–7.
D.A. Foulser, Baer p-elements in translation planes, J. Alg., Vol. 86 (1974), pp. 354–366.
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.
Ch. Hering, On shears of translation planes, Abh. Math. Sem. Univ. Hamburg, Vol. 37 (1972) pp. 258-268.
Ch. Hering, On projective planes of type VI, Atti Convegni Lincei, Vol. 17; Teor. Combinatorie II (1976) pp. 29–53.
M.J. Ganley, Baer involutions in semifields of even order, Geom. Ded., Vol. 2 (1973) pp. 499–508.
M. Ganley, V. Jha and N.L. Johnson, The translation planes admitting a nonsolvable doubly transitive linesized orbit, J. Geom. (to appear).
V. Jha and N.L. Johnson, Regular parallelisms from translation planes, Discrete J. Math., Vol. 59 (1986) pp. 91–97.
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.
V. Jha and N.L. Johnson, Baer involutions in translation planes admitting large elation groups, Results in Math., Vol. 11 (1987) pp. 63–71.
N.L. Johnson, The maximal special linear groups that act on translation planes, Boll. U.M.I., Vol. 6 (1986) pp. 349–352.
N.L. Johnson and T.G. Ostrom, Tangentially transitive planes of order 16, J. Geom., Vol. 10 (1977) pp. 146–163.
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.
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.
W.M. Kantor, Homogeneous designs and geometric lattices, J. Comb. Theory (Series A), Vol. 38 (1985) pp. 66–74.
W. Ljunggren, Einige Bemerkungen über die Darstellung ganzer Zahlen durch binäre kubische Former mit positiver Diskriminante, Acta Math., Vol. 75 (1942) pp. 1–21.
T.G. Ostrom, Linear transformations and collineations of translation planes, J. Alg.,Vol. 3 (1970) pp. 405–416.
T. Penttila and B. Williams, Regular packings in PG(3,q), European Journal of Combinatorics, Vol. 19 (1998) pp. 713–720.
A. Prince, The cyclic parallelisms of PG(3, 5), European J. Combin., Vol. 19 (1998) pp. 613–616.
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Johnson, N.L. Two-Transitive Parallelisms. Designs, Codes and Cryptography 22, 179–189 (2001). https://doi.org/10.1023/A:1008321206709
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DOI: https://doi.org/10.1023/A:1008321206709