Abelian group

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Related to Finite abelian group: Fundamental theorem of finite abelian groups

Abelian group

[ə′bēl·yən ′grüp]
(mathematics)
A group whose binary operation is commutative; that is, ab = ba for each a and b in the group. Also known as commutative group.
References in periodicals archive ?
Examples of such groups are: finite Abelian groups ([12], Theorem 4.
Calderon, Asymptotic estimates on finite abelian groups, Publications De L'institut Mathematique, Nouvelle serie, 74(2003), No.
It is known that the following groups are determined by their endomorphism semigroups in the class of all groups: finite Abelian groups ([6], Theorem 4.
because each finite Abelian group is determined by its endomorphism semigroup in the class of all groups ([7], Theorem 4.
Since (Q, +) and (Q', +') are finite Abelian groups, their isomorphism follows from End(Q, +) [congruent to] End( Q', +') (see Theorem 4.
Some significant information about an integer vector configuration is not retained in the multiplicity function, as many finite abelian groups can have the same cardinality.
Examples of such groups are finite Abelian groups ([4], Theorem 4.
Papers cover such subjects as outer automorphism groups of certain orientable Seifert three-manifold groups, a proposed public key cryptosystem using the modular group, normal subgroups of themodular group and other Hecke groups, unions of varieties and quasi-varieties, context-free irreducible word problems in groups, informative words and discreteness, using group theory for knowledge representation and discovery, torsion in maximal arithmetic Fuchsian groups, density of test elements in finite Abelian groups and the Rosenberg "monster.