Geodesic
Subregular Spreads and Indicator Sets
Canadian journal of mathematics, Tome 27 (1975) no. 5, pp. 1141-1148

Voir la notice de l'article provenant de la source Cambridge University Press

In a previous paper [3] we introduced indicator sets in order to facilitate the study of partial spreads and spreads in ∑ = PG(3, q). The idea enabled us to disprove a conjecture in the literature by constructing a spread that contained no regulus. More recently there have been some notable advances in the theory of spreads. One such advance is Denniston's theorem that packings of spreads always exist in ∑. This result can be very nicely interpreted in terms of indicator sets [1], Another notable advance is the result on subregular spreads due to W. F. Orr [4; 5] which is discussed below. In this note we develop further some ideas on indicator sets in [3] and then use these results to give an alternative proof of this result of Orr. 
Bruen, A. Subregular Spreads and Indicator Sets. Canadian journal of mathematics, Tome 27 (1975) no. 5, pp. 1141-1148. doi: 10.4153/CJM-1975-119-4
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[1] 1. Beutelspacher, A., On parallelisms in 3-dimensional finite projective spaces, to appear, Geometriae Dedicata. Google Scholar

[2] 2. Bruck, R. H., Construction problems ojfinite projective planes, Proceedings of the Conference in Combinatorics held at the University of North Carolina at Chapel Hill, April 10-14, 1967 (University of North Carolina Press, 1969), 426–514. Google Scholar

[3] 3. Bruen, A., Spreads and a conjecture oj Bruck and Bose, J. Algebra 23 (1972), 519–537. Google Scholar

[4] 4. Orr, W. F., A characterization of sub regular spreads infinite 3-space﹜ text of lecture presented to the American Mathematical Society at the Annual Meeting in Dallas, Texas, January 25–29, 1973. (See abstract no. 351, A. M. S. Notices, January 1973.) Google Scholar

[5] 5. Orr, W. F. The miquelian inversive plane IP(q) and the associated projective planes, Doctoral Dissertation, University of Wisconsin, 1973. Google Scholar

[6] 6. Ostrom, T. G., Translation planes, Proc. Conf. on Combinatorial Mathematics and its Applications, Chapel Hill, April 1967 (University of North Carolina Press, Chapel Hill, North Carolina, 1969). Google Scholar

[7] 7. Thas, J., Flocks of finite egglike inversive planes; in Finite geometric structures and their applications, C.I.M.E. II ciclo 1972, Ed. Cremonese, Rome, 1973, pp. 189–191. Google Scholar

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