group G = Z_4 x Z_4
Let H be a subgroup of G of order 4. Explain why H is normal in G and why the quotient group of G by H is Abelian and of order 4.
We seem to be clashing on what the OP is most likely to know today, huh? haha
Of course this is true since the quotient group will be the image of the canonical homomorphism and the image of an abelian group under a homomorphism is always abelian.
The OP will have to decide which he likes better I guess.