Translationsebenen der Ordnung 49 mit einer Quaternionengruppe von Dehnungen. (Translation planes of order 49 with a quaternion group of homologies)
The author shows that there exist, up to isomorphism, exactly ten translation planes of order 49. He solves this problem by finding all systems \(\Sigma\subset GL_ 2(7)\) satisfying the following two conditions 1) for two vectors \(x,y\neq 0\) from \(GF(7)^ 2\) there exists exactly one \(\sigma\in\Sigma\) such that \(\sigma x=y\); 2) \(\Sigma\) contains a group of quaternions \(\Sigma_ 0\) such that \(\Sigma\Sigma_ 0=\Sigma\).
scientific article; zbMATH DE number 92574