Cohomology of Sporadic Simple Groups

Abstract

In this chapter we will describe progress towards understanding the cohomology of the sporadic simple groups. Briefly we recall that from the classification of finite simple groups, [Gor], it was shown that there exist 26 simple groups not belonging to infinite families (i. e. not of alternating or Lie type) and we study ten of these groups here: four of the five Mathieu groups; the Janko groups J ₁, J ₂, J ₃; the O’Nan group O’N; the McLaughlin group McL; and finally the Lyons group Ly.