In
mathematics, an abelian group, also called a commutative group, is a
group (G, * ) with the additional property that the
group operation * is
commutative, so that for all a and b in G, a * b = b * a. Abelian groups are named after
Norwegian mathematician Niels Henrik Abel. Groups in which the group operation is not commutative are called non-abelian (or non-commutative). Since the group operation in an abelian group is commutative as well as associative, the value of a product of group elements is independent of the order in which the product is calculated. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, although infinite abelian groups are the subject of current research.
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