ISSN:
1573-7586
Keywords:
Regulus
;
spread
;
flag-transitive
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract An old conjecture of Bruck and Bose is that every spreadof Σ = PG(3,q) could be obtained by startingwith a regular spread and reversing reguli. Although it was quicklyrealized that this conjecture is false, at least for qeven, there still remains a gap in the spaces for which it isknown that there are spreads which are regulus-free. In severalpapers Denniston, Bruen, and Bruen and Hirschfeld constructedspreads which were regulus–free, but none of these dealtwith the case when q is a prime congruent to onemodulo three. This paper closes that gap by showing that forany odd prime power q, spreads of PG(3,q) yielding nondesarguesian flag-transitive planes are regulus–free.The arguments are interesting in that they are based on elementarylinear algebra and the arithmetic of finite fields.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1018024723184
