## Classification Theorem

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 Order,

2. Alternating Groups of degree at least five,

3. Lie-Type Chevalley Groups , , , 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 15,000 pages in length.

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.