# Abelian group

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## 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 ?
Since each finite Abelian group is determined by its endomorphism semigroup in the class of all groups ([7], Theorem 4.
In fact the two objects are not truly equivalent, in that the information contained in matroids over Z is richer, because there are many finite abelian groups with the same cardinality.
However we shall be concerned with locally compact abelian groups, where the theory has close analogues with the classical theory and is particularly well suited to sampling theory.
Throughout this brief article, let G be an abelian group with p-component of torsion [G.
Fourth Place, a \$25,000 scholarship goes to Alexander `Sasha' Schwartz, 17, of Radnor High School in Radnor, PA, for his mathematics project, "On Coset Partitions of Abelian Groups.
He covers the construction of real and complex numbers, metric and Euclidean spaces, complete metric spaces, normed linear spaces, differentiation, integration, and Fourier analysis on locally compact abelian groups.
The fractal structure of cellular automata on abelian groups.
Let a(n) denote the number of nonisomorphic Abelian groups with n elements.
Mathematicians and scientists discuss such matters as rigid abelian groups and the probabilistic method, looking for indecomposable right bounded complexes, kernel modules of cotorsion pairs, upper cardinal bounds for absolute structures, subgroups of totally projective primary abelian groups and direct sums of cyclic groups, generic endomorphisms of homogeneous structures, special pairs and automorphisms of centerless groups, and some results on the algebraic entropy.
j] of degree r in Z[x], one has an isomorphism of abelian groups
Among the topics discussed by the research articles are symplectic Heegaard splittings and linked abelian groups, differential characters and the Steenrod squares, relative weight filtrations on completions of mapping class groups, symplectic automorphism groups of nilpotent quotient of fundamental groups of surfaces, and new examples of elements in the kernel of the Magnus representation of the Torelli groups.

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