Question

Let G=Z x Z and H={ (a, b) in Z x Z | 8 divides (a+b)...

Let G=Z x Z and H={ (a, b) in Z x Z | 8 divides (a+b) }.

1. Prove that G/H is isomorphic to Z8.

2. What is the index of [G : H]? Explain.

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