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##### Wiktionary
abelian group

alt. (context algebra English) A group in which the group operation is commutative. n. (context algebra English) A group in which the group operation is commutative.

##### Wikipedia
Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written (the axiom of commutativity). Abelian groups generalize the arithmetic of addition of integers. They are named after Niels Henrik Abel.

The concept of an abelian group is one of the first concepts encountered in undergraduate abstract algebra, from which many other basic concepts, such as modules and vector spaces are developed. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood. On the other hand, the theory of infinite abelian groups is an area of current research.

#### Usage examples of "abelian group".

Nearly twenty years before, when he was still a baby in his milk-stained furs, a star in the Abelian Group had exploded into a supernova.