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May 1st, 2011, 01:30 PM   #1
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Nice order problem on subgroups

Let G be a finite group with a normal subgroup N such that |N| and [G: N] are relatively prime. Prove that N is the only subgroup of G whose order is order |N|.
Assume H is a subgroup of G with |H|=|N|, and let a homomorphism go from G to G/N. What does this homomorphism say of the order of the image of H,or H itself?
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May 1st, 2011, 01:56 PM   #2
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Re: Nice order problem on subgroups


What have you tried so far? Did the hints not help?

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