An elementary and unified approach to the Mathieu-Witt systems
Up to now, a great variety of interesting and suggestive studies on the Mathieu-Witt systems \(W_{24}\) and \(W_{12}\) have been made by many people. In particular, Cameron [Parallelismus of complete designs. London Mathematical Society Lecture Notes Series; 23 (1976; Zbl 0333.05007)] and Conway [Three lectures on exceptional groups: In ``Finite simple groups'', 215-247 (1971; Zbl 0221.20014)] studied \(W_{24}\) using symmetric differences effectively, and Curtis [Math. Proc. Cambridge philos. Soc. 79, 25-42 (1976; Zbl 0321.05018)] studied them introducing the somewhat magical concepts of the \(MOG=Miracle\) Octad Generator. Although these studies have revealed many fascinating facts about the systems, it seems that the essence of them is not yet satisfactorily elucidated - for example, it seems that the treatment of both systems is not sufficiently unified and that the way of describing blocks is not so simple. The aim of this article is to present a description of both systems from scratch in as orderly, unified and elementary a manner as possible, using mainly symmetric differences and linear fractional groups PSL(2,q).
scientific article; zbMATH DE number 4214003