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Collineation groups preserving an oval in a projective place of odd order

Part of: Linear incidence geometry Geometry Finite geometry and special incidence structures Permutation groups

Published online by Cambridge University Press:  09 April 2009

Mauro Biliotti  and
Gabor Korchmaros
Mauro Biliotti
Affiliation:
Dipartimento di Matematica, Università di LecceVia Arnesano 73100 Lecce, Italia
Gabor Korchmaros
Affiliation:
Istituto di Matematica Università della BasilicataVia N. Sauro 34 85100 Potenza, Italia
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Abstract

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In this paper we investigate the structure of a collineation group G of a finite projective plane Π of odd order, assuming that G leaves invariant an oval Ω of Π. We show that if G is nonabelian simple, then G ≅ PSL(2, q) for q odd. Several results about the structre and the action of G are also obtained under the assumptions that n ≡ 1 (4) and G is transitive on the points of Ω.

MSC classification

Secondary: 51E15: Affine and projective planes 51A10: Homomorphism, automorphism and dualities 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 1 , February 1990 , pp. 156 - 170
Copyright
Copyright © Australian Mathematical Society 1990

References

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