Is $A_{n-1}$ a normal subgroup of $A_n$? If so, why?
Normal subgroups of the Alternating group $A_n$
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$\begingroup$
abstract-algebra
group-theory
finite-groups
1 Answers
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For $n\geq 5$, $A_n$ is simple, meaning it has no nontrivial normal subgroups.
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1Should it not be 'no non-trivial _proper_ normal subgroups'? – 2019-04-24