A

simple group is a

group with no

normal subgroups other than e (the

trivial group) and itself. The most common examples of simple groups are the

alternating groups A_

*n*, where

*n* > 4.

The classification theorem of finite simple groups states that there are four basic types of finite simple groups, along with twenty-six `sporadic simple groups'. Because of the size (over 15,000 pages) of the proof of this theorem, it is also known as the enormous theorem.