An abelian group is a set, combined with an operation, that satisfies four fundamental properties: closure, associativity, the existence of an identity element, and the existence of inverses for each element. Additionally, in an abelian group, the operation is commutative, meaning the order in which you combine elements does not change the result. This concept is essential in understanding both group theory and the various properties that can arise from groups and their substructures.
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