Journal ArticleDOI
Desarguesian partial parallelisms
TLDR
This article established connections between Desarguesian partial parallelisms of deficiency one in PG(3,q) and translation planes of orderq4 admitting a collineation group isomorphic to SL(2,q), which is generated by Baer collineations.Abstract:
This article establishes connections between Desarguesian partial parallelisms of deficiency one in PG(3,q) and translation planes of orderq4 admitting a collineation group isomorphic to SL(2,q) which is generated by Baer collineations.read more
Citations
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Journal ArticleDOI
Parallelisms of projective spaces
TL;DR: In this paper, new and old results on parallelisms of projective spaces are surveyed, and a survey of parallelism in projective space is also presented, along with a discussion of the relation between parallelism and projectivity.
Journal ArticleDOI
Extended parallelity in spine spaces and its geometry
TL;DR: In this article, the notion of extended parallelity is introduced in an arbitrary spine space, and rudimentary properties of the obtained geometry are presented, including the horizon and dilatation group relative to this parallelity.
Journal ArticleDOI
Regular direct products of affine partial linear spaces
TL;DR: In this article, the class of maximal affine Baer substructures of a Desarguesian affine space was determined, and some interpretations in terms of linear algebra were given.
Journal ArticleDOI
Transversal-Free Translation Nets
Vikram Jha,Norman L. Johnson +1 more
TL;DR: A generalization of the ideas of Bruen shows that any non-Desarguesian spread in PG(3, q) produces a transversal-free net of small deficiency.
Journal ArticleDOI
Transitive Parallelisms
TL;DR: In this paper, the groups acting on parallelisms in PG(3, q), q = pr, which are generated by collineations of order a p-primitive divisor of q3 − 1 are completely determined.
References
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Journal ArticleDOI
Vector spaces and construction of finite projective planes
TL;DR: A survey of work in finite projective planes can be found in this article, with a focus on the work of the authors of the present paper and a discussion of some of the techniques used.
Journal ArticleDOI
Regular Packings of PG (3,q)
Tim Penttila,B. William +1 more
TL;DR: Two regular packings of PG(3,q) are constructed wheneverq?2(mod3) is constructed, with each packing admitting a cyclic group of orderq2+q+1 acting regularly on the regular spreads in the packing.
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The translation planes of order q2 that admit SL(2, q) as a collineation group. I. Even order
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