We wish to classify the factor group $(\mathbb{Z} \times \mathbb{Z})/\langle (2, 2) \rangle$, that is, find a group to which it is isomorphic. (According to the fundamental theorem of finitely generated abelian groups. Initially, I thought the group had but two cosets, forcing an isomorphism to $\mathbb{Z}_2$. Obviously, this is wrong, due to the existence of cosets such as $(1, 0) + \langle (2, 2) \rangle$ However, I am unable to see how I am to find an isomorphism here.
Abstract Algebra – Classifying the Factor Group $(\mathbb{Z} \times \mathbb{Z})/\langle (2, 2) \rangle$
abstract-algebragroup-theory
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