sporadic group

plural sporadic groups

1. group theoryAny one of the 26 exceptional finite simple groups, which do not belong to any of the general, infinite categories specified by the classification theorem for finite simple groups.

   The first five sporadic groups were discovered by Mathieu in the late nineteenth century. The remaining twenty-one were discovered in the nineteen sixties and seventies.

   1998, David J. Benson, “Cohomology of Sporadic Groups, Finite Loop Spaces, and the Dickson Invariants”, in Peter H. Kropholler, Graham A. Niblo, Ralph Stöhr, editors, Geometry and Cohomology in Group Theory, Cambridge University Press, page 10

   2 more examples

   By the classification of finite simple groups in 1981 it is now known that every finite simple group is either cyclic of prime order, or an alternating group of degree 5 or bigger, or a simple group of Lie type as above, or one of 26 sporadic groups.

   1998, Meinolf Geck, “Finite Groups of Lie Type”, in Roger William Carter, Meinolf Geck, editors, Representations of Reductive Groups, Cambridge University Press, page 63

   It is natural to expect that the sporadic groups should play a role in the structure of the Coker(J) space, though we are only beginning to understand some of the smaller sporadic groups in this framework.

   2004, Alejandro Adem, R. James Milgram, Cohomology of Finite Groups, 2nd edition, Springer, page 245