Re: simple groups and permutation groups

On Mon, 31 Mar 2008 00:39:44 EDT, Jack Schmidt
<Jack.Schmidt.SciMath@xxxxxxxxx> wrote:

Let G be a simple group and let f : S_n --> G be a
surjective homomorphism for some positive integer n.

Why is G isomorphic to S_k, for some k =< n ?

Because G is cyclic of order two and n>=2.

Which would make it a trick question.

If that was really the wording of the assigned question then, while
technically not incorrect, I suspect the problem was posed in error.

quasi
.