Let G be a collineation group of a finite projective plane pi of odd order fixing an oval Omega. We investigate the case in which G has even order, has two orbits Omega(0) and Omega(1) on Omega, and the action of G on Omega(0) is primitive. We show that if G is irreducible, then pi has a G-invariant desarguesian subplane pi(0) and Omega(0) is a conic of pi(0).
Irreducible collineation groups with two orbits forming an oval / Aguglia, Angela; Bonisoli, A.; Korchmáros, G.. - In: JOURNAL OF COMBINATORIAL THEORY. SERIES A. - ISSN 0097-3165. - 114:8(2007), pp. 1470-1480. [10.1016/j.jcta.2007.03.001]
Irreducible collineation groups with two orbits forming an oval
AGUGLIA, Angela;
2007-01-01
Abstract
Let G be a collineation group of a finite projective plane pi of odd order fixing an oval Omega. We investigate the case in which G has even order, has two orbits Omega(0) and Omega(1) on Omega, and the action of G on Omega(0) is primitive. We show that if G is irreducible, then pi has a G-invariant desarguesian subplane pi(0) and Omega(0) is a conic of pi(0).File in questo prodotto:
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