Three Lectures on Exceptional Groups

Abstract

The first lecture records certain exceptional properties of the groups L ₂(p) and gives a description of the Mathieu group M ₁₂ and some of its subgroups, followed by a digression on the Janko group J ₁ of order 175560. With the exception of the Janko group material, all the structure described appears within the Mathieu group M ₂₄, which is the subject of the second lecture, where M24 is constructed and its subgroups described in some detail. The information on M ₂₄ is then found useful in the third lecture, on the group Co _o = · 0 and its subgroups. An appendix describes the exceptional simple groups.