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17.13) Find all of the subgroups of Z2 X Z2. The answer is "there are five subgroups", how come?

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I'm pretty sure these are the five subgroups. I'm sure I'll be corrected if I'm wrong.

1. ([0],[0]) = id.

2. {([0],[0]),([0],[1])}

3. {([0],[0]),([1],[0])}

4. {([0],[0]),([1],[1])}

5. Z2 x Z2

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17.13. The second post above has them all. Good.