Displaying similar documents to “Sull'equazione indeterminata x 2 ⁢ n + y 2 ⁢ n = z 2 .”

Alcune condizioni per la costruzione di un piano finito di traslazione

Alessandro Basile, Paolo Brutti (2001)

Bollettino dell'Unione Matematica Italiana

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The construction of any finite translation plane depends on the appropriate determination of a partition P ⁢ E of a Galois field E , together with a set A of automorphisms of E as a vector space. In this paper we obtain sufficient conditions on P ⁢ E and A , so that a translation plane is produced. They are also necessary conditions when A = 1 . Particularly, we examine the case where E is a two-dimensional vector space. We prove that no translation planes are constructible by a single automorphism,...