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Is $A_{n-1}$ a normal subgroup of $A_n$? If so, why?

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up vote 3 down vote accepted

For $n\geq 5$, $A_n$ is simple, meaning it has no nontrivial normal subgroups.

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Should it not be 'no non-trivial proper normal subgroups'? –  user50229 Dec 4 '12 at 20:41

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