Describe all subgroups of order ≤ 4 of ℤ4 × ℤ4, and in each case classify the factor group of ℤ4 × ℤ4 modulo the subgroup by Theorem 11.12. That is, describe the subgroup and say that the factor group of ℤ4 × ℤ4 modulo the subgroup is isomoiphic to ℤ2 × ℤ4, or whatever the case may be. [Hint: ℤ2 × ℤ4 has six different cyclic subgroups of order 4. Describe them by giving a generator, such as the subgroup 〈(1, 0)〉. There is one subgroup of order 4 that is isomorphic to the Klein 4-group. There are three subgroups of order 2.]
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