A fantasia on quaternions and near-fields
This is a nice exposition written in a leisurely way, about the connection between Hamilton's skewfield, the quaternion group \(Q_8\) and the smallest nearfield \(K\) with 9 elements. It is proven that \((K_.^*)\cong Q_8\). Indeed the author deplores that most mathematicians (and even some algebraist) do not know what a nearfield is. Lam explains the historical background around the invention of the quaternions by Hamilton and the nearfields by Dickson and adds remarks about the importance of nearfields in the study of projective planes as well as the close relations to doubly transitive Frobenius groups (i.e. sharply 2-transitive permutation groups). (The reviewer likes to add the analogue: most mathematical libraries do not possess the standard reference on nearfields: \textit{H. Wähling}'s Theorie der Fastkörper, Thales Verlag, Essen (1987; Zbl 0669.12014), which has an excellent English written summary in which each definition and each theorem can be found in an English translation).
scientific article; zbMATH DE number 1151671