J Austral Math Soc Ser A 48 pp156--170, 1990.

Collineation Groups Preserving an Oval in a Projective Plane of Odd Order

Mauro Biliotti and Gabor Korchmaros

Abstract

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

1980 AMS Subject Classification (1985 Revision): primary 51E15, 51A10; secondary 20B25

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Authors

Mauro Biliotti

Dipartimento di Matematica, Università di Lecce, Via Arnesano, 73100 Lecce, Italia.

Gabor Korchmaros

Istituto di Matematica, Università della Basilicata, Via N. Sauro 34, 85100 Potenza, Italia.