The classification theorem of finite simple groups, also known as the "enormous theorem," which
states that the finite simple
groups can be classified completely into
1. Cyclic groups of prime group
2. Alternating groups of degree at least five,
3. Lie-type Chevalley groups given by , , , and ,
4. Lie-type (twisted Chevalley groups or the Tits group) , , , , , , , , ,
5. Sporadic groups , , , , , , Suz, HS, McL, , , , He, , , , HN, Th, , , , O'N, , Ly, Ru, .
The "proof" of this theorem is spread throughout the mathematical literature and is estimated to be approximately pages in length.
See alsoFinite Group
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ReferencesCartwright, M. "Ten Thousand Pages to Prove Simplicity." New Scientist 109, 26-30, 1985.Cipra, B. "Are Group
Theorists Simpleminded?" What's
Happening in the Mathematical Sciences, 1995-1996, Vol. 3. Providence,
RI: Amer. Math. Soc., pp. 82-99, 1996.Cipra, B. "Slimming
an Outsized Theorem." Science 267, 794-795, 1995.Gorenstein,
D. "The Enormous Theorem." Sci. Amer. 253, 104-115, Dec.
1985.Solomon, R. "On Finite Simple Groups and Their Classification."
Not. Amer. Math. Soc. 42, 231-239, 1995.Wells, D. The
Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England:
Penguin Books, p. 57, 1986.
Referenced on Wolfram|AlphaClassification Theorem
of Finite Groups
Cite this as:
Weisstein, Eric W. "Classification Theorem of Finite Groups." From MathWorld--A Wolfram Web Resource.