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