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May 1st, 2011, 01:30 PM  #1 
Newbie Joined: May 2011 Posts: 9 Thanks: 0  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. Hint: 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? 
May 1st, 2011, 01:56 PM  #2 
Senior Member Joined: Jun 2010 Posts: 618 Thanks: 0  Re: Nice order problem on subgroups
matheart, What have you tried so far? Did the hints not help? Ormkärr 

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