Classification of finite simple groups
The
classification of the finite simple groups is a vast body of work in
mathematics, mostly published between around 1955 and 1983, which classifies all of the finite simple groups. In all, the work comprises about 10,000 - 15,000 pages in 500 journal articles by some 100 authors. However, there is a controversy in the mathematical community on whether these articles provide a complete and correct proof.
The classification shows every finite simple group to be one of the following types:
The Sporadic Groups
Five of the sporadic groups were discovered by Mathieu in the 1860s and the other 21 were found between 1965 and 1975. The full list is:
- Mathieu groupss M11, M12, M22, M23, M24
- Janko groups J1, J2, J3, J4
- Conway groups Co1, Co2, Co3
- Fischer groups F22, F23, F24
- Higman-Sims group HS
- McLaughlin group McL
- Held group He
- Rudvalis group Ru
- Suzuki sporadic group Suz
- O'Nan group ON
- Harada-Norton group HN
- Lyons group Ly
- Thompson group Th
- Baby Monster group B
- Monster group M
References
- Ron Solomon: On Finite Simple Groups and their Classification, Notices of the American Mathematical Society, February 1995
- Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A.: "Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups." Oxford, England 1985.