Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-27T20:44:25.488Z Has data issue: false hasContentIssue false
  • English
  • Français

Indicator Sets, Reguli, and a New Class of Spreads

Published online by Cambridge University Press:  20 November 2018

F. A. Sherk  and
Günther Pabst
F. A. Sherk
Affiliation:
University of Toronto, Toronto, Ontario
Günther Pabst
Affiliation:
University of Toronto, Toronto, Ontario
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let Σ be the projective 3-space over the field GF(q) where q = pe, p an odd prime. A spread W in ∑ is a set of q2 + 1 lines in ∑ which are such that each point of Σ lies on exactly one line of W. Thus the lines of W are all mutually skew. The notion of a spread extends to higher dimensions and also applies for arbitrary fields [1; 3; 6, p. 29; 7, p. 5]. Our concern, however, will be within the narrower but still extensive bounds indicated.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 1 , 01 February 1977 , pp. 132 - 154
Copyright
Copyright © Canadian Mathematical Society 1977

Footnotes

This paper was written while the first author was on sabbatical leave at Washington State University.

References

1. André, J., Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe, Math. Zeit. 60 (1954), 156–186.Google Scholar
2. Bruck, R. H., Construction problems of finite 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).Google Scholar
3. Bruck, R. H. and Bose, R. C., The construction of translation planes from projective spaces, J. Algebra 1 (1964), 85–102.Google Scholar
4. Bruen, A., Spreads and a conjecture of Bruck and Bose, J. Algebra 23 (1972), 519–537.Google Scholar
5. Coxeter, H. S. M., Introduction to geometry (Wiley, New York, 1961).Google Scholar
6. Dembowski, P., Finite geometries (Springer-Verlag, Berlin, 1968).CrossRefGoogle Scholar
7. Ostrom, T. G., Finite translation planes (Springer-Verlag, Berlin, 1970).10.1007/BFb0070676CrossRefGoogle Scholar
7. Ostrom, T. G. Classification of finite translation planes, Proceedings of the international conference on projective planes held at Washington State University, April 25–28, 1973 (Washington State University Press, 1973).Google Scholar
9. Veblen, O. and Young, J. W., Projective geometry, Vol. I (Ginn, Boston, 1910).Google Scholar