A characterization of classical Minkowski planes over a perfect field of characteristic two |
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Authors: | Miklos Percsy |
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Institution: | 1. Faculté de Médecine Service de Mathématique, Université de l'Etat de Mons, avenue Maistriau, 15, 7000, Mons, Belgium
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Abstract: | We give a new set of axioms defining the concept of (B*)-plane (i.e. Minkowski plane without the tangency property) and we show that every (B*)-plane in which a condition similar to the “Fano condition” of Heise and Karzel (see 5, § 3]) holds, is a Minkowski plane over a perfect field of characteristic two. In particular, every finite (B*)-plane of even order is a Minkowski plane over a field. Consequences for strictly 3-transitive groups are derived from the preceding results; in particular, every strictly 3-transitive set of permutations of odd degree containing the identity is a protective group PGL2(GF(2 n )) over a finite field GF(2 n , for some positive integer n. |
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