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Transitive Partial Parallelisms of Deficiency One

✍ Scribed by Norman L. Johnson; Rolando Pomareda

Book ID: 102570981
Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 266 KB
Volume: 23
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2002.0608

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✦ Synopsis

A new construction of parallelisms, determined by Johnson, is valid for both the finite and infinite cases and gives a variety of partial parallelisms of deficiency one that admit a transitive group. Since there are extensions to parallelisms, one obtains parallelisms admitting a collineation group fixing one spread and transitive on the remaining spreads. The construction permits a counting of the isomorphism classes of the parallelisms. In this article, we enumerate the isomorphism classes of the parallelisms and show that there are at least 1 + [(q -3)/2r] mutually non-isomorphic parallelisms in PG(3, q = p r ), for p odd. Furthermore, we provide a group-theoretic characterization of the constructed parallelisms.

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