Let G be a finite group of even order with n elements. H is a subgroup of G, with n/2 elements.(adsbygoogle = window.adsbygoogle || []).push({});

I need to show that H is normal. I have set up the phi function to be: phi(x) = 1 if x is an element of H. phi(x) = -1 if x is not an element of H. Thus H is the kernal.

I am trying to show that H is a homomorphism. Then from that I know that H is normal.

I am breaking this up into cases. I have been successful showing that the homomorphism holds if x,y are both in H. It also holds if x is in H and y is in G.

However, I am having difficulty showing that if x and y are both in G, then their product xy must be in H. How do I go about showing that?

Colleen

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# Another homomorphism question

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