abelian group

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a·be·li·an group

[After Niels Henrik Abel (1802-1829), Norwegian mathematician.]

Abelian group

(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 ?
digital representations of real numbers), and for recognizing some sets of integers or more generally of finitely generated abelian groups or monoids.
Among the topics are greatest common divisors, integer multiples and exponents, quotients of polynomial rings, divisibility and factorization in integral domains, subgroups of cyclic groups, cosets and Lagrange's theorem, the fundamental theorem of finite abelian groups, and check digits.
A quasi-arithmetic matroid endows a matroid with a multiplicity function, whose values (in the representable case) are the cardinalities of certain finite abelian groups, namely, the torsion parts of the quotients of an ambient lattice [Z.
We define a(n) to be the number of nonisomorphic Abelian groups with n elements.
de Vries: Intuitionistic free abelian groups, Math.
Considering another category, the category of Abelian groups [A.
Many of the important properties of Fourier transforms on locally compact abelian groups are proved to hold true for F.
Their topics include financial markets, polynilpotent multipliers of finitely generated abelian groups, the concept of subtype in Bernstein algebras, optimal processes in irreversible microeconomics, algebraic solutions for matrix games, methods of drawing special curves and surfaces, some game theory and financial contracting issues in large corporate transactions, endomorphisms and endomorphism semigroups of groups, the noiseless coding theorem, odd zeta and other special function bounds, and spectral properties of discrete Schrodinger operator with quasi-periodically recurrent potential.
Lehmer, A ternary analogue of abelian groups, American Journal of Mathematics, 54:329-338, 1932.
Key words and phrases: Whittaker-Kotel'nikov-Shannon theorem, Plancherel's formula, locally compact abelian groups, discrete subgroups, tranvsersals
Therefore abelian groups are completely characterized as subtractive groupoids.