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On a New Family of Flag-transitive Semibiplanes

✍ Scribed by Antonio Pasini; Satoshi Yoshiara

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 200 KB
Volume: 22
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2001.0502

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✦ Synopsis

Each of the d-dimensional dual hyperovals S h m discovered by Yoshiara [20] gives rise, via affine expansion, to a flag-transitive semibiplane A f (S h m ). We prove that, if m

is not isomorphic to any of the examples we are aware of, except possibly for certain semibiplanes obtained from D n -buildings defined over G F(2). However, many semibiplanes live hidden as quotients inside halved hypercubes. It is thus quite natural to ask whether any of our semibiplanes are like that. We prove that A f (S h m ) is a quotient of a halved hypercube if and only if h = m.

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