sporadic group

English

Etymology

The earliest usage is thought to be that of English mathematician William Burnside in 1911, W. Burnside, Theory of Groups of Finite Order, 2nd Edition, in a comment about the Mathieu groups.

Noun

sporadic group (plural sporadic groups)

1. (group theory) Any 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.
   • 1998, Meinolf Geck, “Finite Groups of Lie Type”, in Roger William Carter, Meinolf Geck, editors, Representations of Reductive Groups, Cambridge University Press, page 63:

     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, 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:

     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.

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

     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.

Usage notes

The largest sporadic group is called the monster group (or Fischer–Griess monster group). All but six of the other groups are subquotients of the monster group; together with the latter, they form the Happy Family. The remaining six are called pariah groups.

Hyponyms

• (exceptional finite simple group): baby monster group, Conway group, Fischer group, Fischer–Griess monster group (= monster group), Harada–Norton group, Held group, Janko group, Lyons group, McLaughlin group, Mathieu group, monster group, Higman–Sims group, O'Nan group, pariah group, Rudvalis group, Suzuki group, Thompson group

Translations

exceptional finite simple group

See also

• happy family