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More on the group Y555 and the projective plane of order 3

โœ Scribed by Leonard H Soicher

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
330 KB
Volume
136
Category
Article
ISSN
0021-8693

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๐Ÿ“œ SIMILAR VOLUMES

More on the existence of small quasimult
More on the existence of small quasimultiples of affine and projective planes of arbitrary order
โœ Alan C. H. Ling ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 112 KB

## Abstract The functions __a(n)__ and __p(n)__ are defined to be the smallest integer ฮป for which ฮปโ€fold quasimultiples affine and projective planes of order __n__ exist. It was shown by Jungnickel [J. Combin. Designs 3 (1995), 427โ€“432] that __a(n),p(n)__โ€‰<โ€‰__n__^10^ for sufficiently large __n__.

The nonexistence of projective planes of
The nonexistence of projective planes of order 12 with a collineation group of order 8
โœ Kenzi Akiyama; Chihiro Suetake ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 183 KB

## 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. A

On the existence of small quasimultiples
On the existence of small quasimultiples of affine and projective planes of arbitrary order
โœ Dieter Jungnickel ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 798 KB

Denote by a(n) and p(n), respectively, the smallest positive integers ,I and p for which an &(2, n, n') and an S,,(2, n + 1, n2 + n + 1) exist. We thus consider the problem of the existence of (nontrivial) quasimultiples of atline and projective planes of arbitrary order n. The best previously known