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EnglishA result of Dempwolff [4] asserts that a projective plane Π of order q3 admitting G =PGL(3, q) as a collineation group contains a G-invariant subplane π_0 isomorphic to PG(2, q) on which G acts 2-transitively. Moreover, G splits the point set and the line set of Π into 3 orbits P_i(Π) and L_i(Π), i = 1, 2, 3, consisting of the points (respectively lines) of Π incident with q + 1, 1 or 0 lines (respectively points) of π_0. In this paper it is proven that Π is either the desarguesian or the Figueroa plane of order q^3 if, and only if, (P_3(Π), L_3(Π)) is isomorphic to (P_3(D), L_3(D)), where D = PG(2, q^3).
| Titolo: | A new characterization of the desarguesian and the Figueroa plane |
| Autori: | |
| Data di pubblicazione: | 2019 |
| Rivista: | |
| Abstract: | A result of Dempwolff [4] asserts that a projective plane Π of order q3 admitting G =PGL(3, q) as a collineation group contains a G-invariant subplane π_0 isomorphic to PG(2, q) on which G acts 2-transitively. Moreover, G splits the point set and the line set of Π into 3 orbits P_i(Π) and L_i(Π), i = 1, 2, 3, consisting of the points (respectively lines) of Π incident with q + 1, 1 or 0 lines (respectively points) of π_0. In this paper it is proven that Π is either the desarguesian or the Figueroa plane of order q^3 if, and only if, (P_3(Π), L_3(Π)) is isomorphic to (P_3(D), L_3(D)), where D = PG(2, q^3). |
| Handle: | http://hdl.handle.net/11587/437256 |
| Appare nelle tipologie: | Articolo pubblicato su Rivista |
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