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. The classification shows every finite simple group to be one of the following types:
5 of the sporadic groups were discovered by Mathieu in the 1860's and the other 21 were found between 1965 and 1975. The full list is:
- Mathieu groups[?] M_{11}, M_{12}, M_{22}, M_{23}, M_{24}
- Janko groups[?] J_{1}, J_{2}, J_{3}, J_{4}
- Conway groups[?] Co_{1},Co_{2},Co_{2}
- Fischer groups[?] F_{22},F_{23},F_{24}
- 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[?]
- Monster group M
External links and references:
- Ron Solomon: On Finite Simple Groups and their Classification (http://www.ams.org/notices/199502/solomon.pdf), 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.
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