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Mathematics

An (n>4) Is A Simple Group
Theorem: An is simple for n>4
Suppose H is a normal subgroup of An, and H is not {e} Then H contains a three cycle.
Therefore H contains every three cycle of An
Then, every element of An is a product of three cycles, An being generated by three cycles.
So, An is a subgroup of or is equal to H (H contains An)
therefore since H is contained in An, H = An (H is isomorphic to An)
An is simple for n>4.
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