- Abelian group
- A group in which the group operation is commutative. It is important in the study of rings and vector spaces.

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**Abelian group**— [ə bē′lē ən, əbēl′yən] n. 〚after Niels H. Abel (1802 29), Norw mathematician〛 Math. a commutative group * * * … Universalium**Abelian group**— [ə bē′lē ən, əbēl′yən] n. [after Niels H. Abel (1802 29), Norw mathematician] Math. a commutative group … English World dictionary**Abelian group**— For other uses, see Abelian (disambiguation). Abelian group is also an archaic name for the symplectic group Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product,… … Wikipedia**Abelian group**— noun a group that satisfies the commutative law • Syn: ↑commutative group • Hypernyms: ↑group, ↑mathematical group … Useful english dictionary**abelian group**— noun a group in which the group operation is commutative Syn: commutative group … Wiktionary**Free abelian group**— In abstract algebra, a free abelian group is an abelian group that has a basis in the sense that every element of the group can be written in one and only one way as a finite linear combination of elements of the basis, with integer coefficients … Wikipedia**Finitely-generated abelian group**— In abstract algebra, an abelian group (G,+) is called finitely generated if there exist finitely many elements x1,...,xs in G such that every x in G can be written in the form x = n1x1 + n2x2 + ... + nsxs with integers n1,...,ns. In this case, we … Wikipedia**Finitely generated abelian group**— In abstract algebra, an abelian group ( G ,+) is called finitely generated if there exist finitely many elements x 1,..., x s in G such that every x in G can be written in the form : x = n 1 x 1 + n 2 x 2 + ... + n s x s with integers n 1,..., n… … Wikipedia**Rank of an abelian group**— In mathematics, the rank, or torsion free rank, of an abelian group measures how large a group is in terms of how large a vector space over the rational numbers one would need to contain it; or alternatively how large a free abelian group it can… … Wikipedia**Elementary abelian group**— In group theory an elementary abelian group is a finite abelian group, where every nontrivial element has order p where p is a prime.By the classification of finitely generated abelian groups, every elementary abelian group must be of the form:(… … Wikipedia