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Simple group

Definition

A non-trivial group $G$ is said to be simple if its only normal subgroups are itself and the trivial subgroup.

Properties

TODO

Types

The finite simple groups can be classified into several families:

• Prime cyclic groups $C_p$.
• Alternating groups $A_n$ for $n \ge 5$.
• Groups of lie type.
• 26 sporadic simple groups. The smallest has order 7920 and the largest, "the Monster", has order 808017424794512875886459904961710757005754368000000000.

all these pages adapted with probably insufficient credit from my university's lecture notes