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Spreads which are Not Dual Spreads

Published online by Cambridge University Press:  20 November 2018

A. Bruen  and
J. C. Fisher
A. Bruen
Affiliation:
University of Toronto
J. C. Fisher
Affiliation:
University of Toronto
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In this note we show the existence of a spread which is not a dual spread, thus answering a question in [1]. We also obtain some related results on spreads and partial spreads.

Let ∑ = PG(2t-l, F) be a projective space of odd dimension (2t-l, ≥2) over the field F. In accordance with [1] we make the following definitions. A partial spread S of ∑ is a collection of (t-l)-dimensional projective subspaces of ∑ which are pairwise disjoint (skew).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 6 , December 1969 , pp. 801 - 803
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Bruck, R.H. and Bose, R.C., The construction of translation planes from projective spaces. J. Algebra 1 (1964) 85–102.Google Scholar
2. Bruen, A., Blocking sets in finite projective planes, (unpublished).Google Scholar
3. Dembowski, P., Finite eometries (Springer-Verlag, 1968).Google Scholar
4. Mesner, D. M., Sets of disjoint lines in PG(3, q). Canad. J. Math. 19 (1967) 273–280.Google Scholar