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.
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