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Can anyone come up with an alternative proof of the following?

If H, a subgroup of G, has index [G]=p where p is the smallest prime dividing |G|, the H is normal in G.

I'm already aware of one proof, given here

http://www.math.rochester.edu/courses/236H/home/hw8sol.pdf [Broken]

(page 3 - question #3)

but I'm hoping to find maybe a more straightforward proof.

If H, a subgroup of G, has index [G]=p where p is the smallest prime dividing |G|, the H is normal in G.

I'm already aware of one proof, given here

http://www.math.rochester.edu/courses/236H/home/hw8sol.pdf [Broken]

(page 3 - question #3)

but I'm hoping to find maybe a more straightforward proof.

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