abelian group


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Related to abelian group: group theory, vector space, Cyclic group

a·be·li·an group

 (ə-bē′lē-ən)
[After Niels Henrik Abel (1802-1829), Norwegian mathematician.]

Abelian group

(əˈbiːlɪən)
n
(Mathematics) a group the defined binary operation of which is commutative: if a and b are members of an Abelian group then ab = ba
[C19: named after Niels Henrik Abel (1802–29), Norwegian mathematician]
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.Abelian group - a group that satisfies the commutative lawAbelian group - a group that satisfies the commutative law
mathematical group, group - a set that is closed, associative, has an identity element and every element has an inverse
References in periodicals archive ?
It is well known that all endomorphisms of an Abelian group form a ring and many of its properties can be characterized by this ring.
Let ZV denote the free abelian group on the vertices in V.
Our scheme is based on elliptic curve cryptography whose security relies on the difficulty to solve the discrete logarithm problem of the elliptic curve abelian group (The Elliptic Curve Discrete Logarithm Problem, ECDLP).
A] (V, W) is the additive abelian group of all homomorphisms from V to W, The same notation will be used in case V, Ware left A modules.
The approach in [12] culminates in the deep investigation of Balan, Casazza, Heil, and Landau [1, 2] who have found a density theory for a general class of frames that are labeled by a discrete Abelian group.
1) This of course refers to a particular type of multiplicative Abelian group in Number Theory, and not the television series Star Trek.
This is what is called a free abelian group, where the second word derives from the name of the Norwegian mathematician Abel.
This note shows how to obtain an abelian group with an addition like operation (Joyner 2002:70-72) beginning with a subtraction binary operation.
The second conjecture concerns the study of infinite almost abelian groups, more precisely we ask whether the super tree property at a small cardinal kappa implies that every almost free abelian group of size kappa is free.
Moreover, the notion of bond lattice comes from the study of Galois connections, and a natural action of set partitions that is analogous to the action of integers on any abelian group.