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The Cyclic Parallelisms of PG(3,5)

โœ Scribed by A.R. Prince

Book ID
102567216
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
78 KB
Volume
19
Category
Article
ISSN
0195-6698

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โœฆ Synopsis

We determine, by a computer search, all the cyclic parallelisms of PG(3, 5). There are 45 of them, up to projective equivalence. In particular, there are two cyclic regular parallelisms of PG(3, 5). Previously, no example was known of a regular parallelism in PG(3, q), for q odd.

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A t-vY kY k design is a set of v points together with a collection of its k-subsets called blocks so that all subsets of t points are contained in exactly k blocks. The d-dimensional projective geometry over GFqY PGdY q, is a 2 ร€ q d q dร€1 ร ร ร q 1Y q 1Y 1 design when we take its points as the poin