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.
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Titolo: | On finite projective planes in Lenz-Barlotti class at least I.3 | |
Autori: | ||
Data di pubblicazione: | 2003 | |
Rivista: | ||
Handle: | http://hdl.handle.net/11573/29975 | |
Appartiene alla tipologia: | 01a Articolo in rivista |