Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - October 1989 - Volume 32, Issue 03  

Research Article

Further elementary techniques using the miracle octad generator

R. T. Curtis

In this paper we describe various techniques, some of which are already used by devotees of the art, which relate certain maximal subgroups of the Mathieu group M24, as seen in the MOG, to matrix groups over finite fields. We hope to bring out the wealth of algebraic structure underlying the device and to enable the reader to move freely between these matrices and permutations. Perhaps the MOG was mis-named as simply an “octad generator”; in this paper we intend to show that it is in reality a natural diagram of the binary Golay code.

(Received July 20 1987)