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The nonexistence of projective planes of order 12 with a collineation group of order 8

✍ Scribed by Kenzi Akiyama; Chihiro Suetake

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 183 KB
Volume: 16
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20175

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✦ Synopsis

Abstract

In this article, we prove that there does not exist a symmetric transversal design ${\rm STD}_2[12;6]$ which admits an automorphism group of order 4 acting semiregularly on the point set and the block set. We use an orbit theorem for symmetric transversal designs to prove our result. As a corollary of the result, we prove that there is no projective plane of order 12 admitting a collineation group of order 8. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 411–430, 2008

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