Regulus-free Spreads of PG(3, q)

R. D. Baker and G. L. Ebert
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R. D. Baker: West Virginia State College, Department of Mathematics
G. L. Ebert: University of Delaware, Department of Mathematical Sciences

A chapter in Designs and Finite Geometries, 1996, pp 79-89 from Springer

Abstract: Abstract An old conjecture of Brack and Bose is that every spread of Σ = PG(3, q) could be obtained by starting with a regular spread and reversing reguli. Although it was quickly realized that this conjecture is false, at least for q even, there still remains a gap in the spaces for which it is known that there are spreads which are regulus-free. In several papers Denniston, Bruen, and Bruen and Hirschfeld constructed spreads which were regulus-free, but none of these dealt with the case when p is a prime congruent to one modulo three. This paper closes that gap by showing that for any odd prime power p, spreads of PG(3, p) yielding nondesarguesian flag-transitive planes are regulus-free. The arguments are interesting in that they are based on elementary linear algebra and the arithmetic of finite fields.

Keywords: Regulus; spread; flag-transitive (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-1-4613-1395-3_5

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