Let G be a collineation group of a finite projective plane P of odd order fixing an oval Ω. We investigate the case in which G has even order, has two orbits Ω_0 and Ω_1 on Ω, and the action of G on Ω_0 is primitive.We show that if G is irreducible, then P has a G-invariant desarguesian subplane P_0 and Ω_0 is a conic of P_0.
Irreducible collineation groups with two orbits forming an oval / A., Aguglia; Bonisoli, Arrigo; G., Korchmaros. - In: JOURNAL OF COMBINATORIAL THEORY. SERIES A. - ISSN 0097-3165. - STAMPA. - 114:8(2007), pp. 1470-1480. [10.1016/j.jcta.2007.03.001]
Irreducible collineation groups with two orbits forming an oval
BONISOLI, Arrigo;
2007
Abstract
Let G be a collineation group of a finite projective plane P of odd order fixing an oval Ω. We investigate the case in which G has even order, has two orbits Ω_0 and Ω_1 on Ω, and the action of G on Ω_0 is primitive.We show that if G is irreducible, then P has a G-invariant desarguesian subplane P_0 and Ω_0 is a conic of P_0.
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