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Let G = Z x Z and H = {(a, b) in Z x Z...

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Advance Math

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

a. Prove directly that H is a normal subgroup in G (use the factthat closed under composition and inverses)

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

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

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Recall someBasic factsFor any integer divides that is If then If and then for arbitrary integers and    See Answer
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