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# Classification Theorem of Finite Groups

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

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.

Finite Group, Group, j-Function, Simple Group

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## References

Cartwright, 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|Alpha

Classification Theorem of Finite Groups

## Cite this as:

Weisstein, Eric W. "Classification Theorem of Finite Groups." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ClassificationTheoremofFiniteGroups.html