We establish the connections between finite projective planes admitting a collineation group of Lenz–Barlotti type I.3 or I.4, partially transitive planes of type (3) in the sense of Hughes, and planes admitting a quasiregular collineation group of type (g) in the Dembowski– Piper classification; our main tool is an equivalent description by a certain type of di¤erence set relative to disjoint subgroups which we will call a neo-di¤erence set. We then discuss geometric properties and restrictions for the existence of planes of Lenz–Barlotti class I.4. As a side result, we also obtain a new synthetic description of projective triangles in desarguesian planes.

On finite projective planes in Lenz-Barlotti class at least I.3 / Ghinelli, Dina; D., Jungnickel. - In: ADVANCES IN GEOMETRY. - ISSN 1615-715X. - STAMPA. - -:(2003), pp. S28-S48.

On finite projective planes in Lenz-Barlotti class at least I.3

GHINELLI, Dina;
2003

Abstract

We establish the connections between finite projective planes admitting a collineation group of Lenz–Barlotti type I.3 or I.4, partially transitive planes of type (3) in the sense of Hughes, and planes admitting a quasiregular collineation group of type (g) in the Dembowski– Piper classification; our main tool is an equivalent description by a certain type of di¤erence set relative to disjoint subgroups which we will call a neo-di¤erence set. We then discuss geometric properties and restrictions for the existence of planes of Lenz–Barlotti class I.4. As a side result, we also obtain a new synthetic description of projective triangles in desarguesian planes.
2003
01 Pubblicazione su rivista::01a Articolo in rivista
On finite projective planes in Lenz-Barlotti class at least I.3 / Ghinelli, Dina; D., Jungnickel. - In: ADVANCES IN GEOMETRY. - ISSN 1615-715X. - STAMPA. - -:(2003), pp. S28-S48.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/29975
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