NOT HOMEWORK. 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.