Is it true that when $n \geq 5$ there is a surjective homomorphism from the symmetric group $S_n$ to $S_{n-1}$? How come this is so? Does it have to deal with the subgroup $A_n$ being simple?
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The kernel of a surjective homomorphism from $S_5$ to $S_4$ would have to be of order $5$, but $S_5$ does not have a normal subgroup of order $5$, – Mar 16 '16 at 00:42
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ah so is it when n $\leq$ 4 we will have a surjective homomorphism between $S_n$ and $S_{n-1}$ – WheelofSnow Mar 16 '16 at 00:43