Abelian group theory is a branch of abstract algebra that focuses on the study of Abelian groups (or commutative groups). An **Abelian group** is a set equipped with an operation that satisfies certain properties: 1. **Closure**: For any two elements \( a \) and \( b \) in the group, the result of the operation (usually denoted as \( a + b \) or \( ab \)) is also in the group.
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