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On collineation groups of a projective plane of prime order

โœ Scribed by Chat Yin Ho; Adilson Goncalves

Publisher
Springer
Year
1986
Tongue
English
Weight
463 KB
Volume
20
Category
Article
ISSN
0046-5755

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โœฆ Synopsis

Towards the study of finite projective plane of prime order, the following result is proved in this paper. Let 7r be a projective plane of prime order p and let G be a collineation group of n. If P[I G I, then either n is Desarguesian or the maximal normal subgroup of G is not trivial. In particular, 7z is Desarguesian if G does not leave invariant any point or line. * Partially supported by NSERC A8460. ** Partially supported by CNPq.

๐Ÿ“œ SIMILAR VOLUMES

Collineation groups preserving a unital
Collineation groups preserving a unital in a projective plane of even order
โœ Mauro Biliotti; Gabor Korchmaros ๐Ÿ“‚ Article ๐Ÿ“… 1989 ๐Ÿ› Springer ๐ŸŒ English โš– 576 KB

We investigate the structure of a collineation group G leaving invafiant a unital q/in a finite projective plane II of even order n = m 2. When G is transitive onthe points of ~//and the socle of G has even order, then II must be a Desarguesian plane, ~ a classical unital and PSU(3,m 2) ~< G ~< PFU(

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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