On finite projective planes in Lenz–Barlotti class at least I.3
نویسندگان
چکیده
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.
منابع مشابه
On finite projective planes in Lenz-Barlotti class at least 1.3
We establish the connections between finite projective planes admitting a collineation group of Lenz-Barlotti type 1.3 or 1.4, partially transitive planes of type (3) in the sense of Hughes, and planes admitting a quasiregular collineation group of type (g) in the DembowskiPiper classification; our main tool is an equivalent description by a certain type of difference set relative to disjoint s...
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