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3. a) Suppose that H is a proper subgroup of Z that contains 12, 30, and...

3. a) Suppose that H is a proper subgroup of Z that contains 12, 30, and 54. What are the possibilities for what H could be?

(HINT: You may use without proof that all subgroups of Z are of the formnZ. We will prove this fact later in the semester.)

b) Now, suppose that H is a proper subgroup of Z that contains a and b. What are the possibilities for what H could be?

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