For $n\geq2$, prove that $A_n$ is the only subgroup of $S_n$ with index two.

Asked May 26 '20 at 16:29

Active May 26 '20 at 16:40

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For $n\geq2$, prove that $A_n$ is the only subgroup of $S_n$ with index two. Where $A_n$ is the alternate group with $n$ elements.

edited May 26 '20 at 16:40

user1729

asked May 26 '20 at 16:29

What have you tried? For example, have you considered the intersection of a subgroup $H$ of index two with the subgroup $A_n$? – user1729 May 26 '20 at 16:32
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Welcome to math.se. Please note that we generally do not approve of posts whose entire content is simply the statement of a problem. You should provide context (where you found the problem, what your level is) and tell us about what you’ve attempted or why you are stuck. This ensures that the answers are at the appropriate level and do not repeat things that you already know. Also, please use MathJax. – Arturo Magidin May 26 '20 at 16:32
This question is probably a better duplicate target. If anyone wants to reopen it and close it again then that would be nice, but I've already used up my close vote here... – user1729 May 26 '20 at 16:40

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