digital representations of real numbers), and for recognizing some sets of integers or more generally of finitely generated

abelian groups or monoids.

Some of such groups are finite

Abelian groups ([7], Theorem 4.

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.