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I know how to embed Sn into An+2, just with the extra transposition, etc...

But how to show it can not be embedded into An+1. We don't have the extra transposition.

Using Lagrange's Theorem, we can say when n+1 is odd, then n! does not divide (n+1)!/2 therefore a subgroup of order n! can not exist in An+1.

However, we must also not use Lagrange's Theorem.

Any help?

Thank you.