classification theorem of finite simple groups@Everything2.com

Every finite simple group falls into one of five categories:

Cyclic groups of prime order.
Alternating groups A_n, n > 4.
Chevalley groups.
Twisted Chevalley groups or the tits group (these and the Chevally groups are all Lie-type groups).
The sporadic simple groups; these are the leftovers. They number 26. The most complicated is the monster simple group.

This theorem is also known as the `enormous theorem'; its proof is spread throughout the mathematics literature and is estimated to be over 15,000 pages in length. The proof was finally completed in the early- to mid-1980s.

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