A characterization of divisible and torsion

Abelian groups by their endomorphism semigroups.

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.

Rankin, On the number of

abelian groups of a given order, Quart J.

Romano: Construction of free

abelian groups, Sarajevo J.

1] is compact), and so are united by working with locally compact

abelian groups.

This note shows how to obtain an

abelian group with an addition like operation (Joyner 2002:70-72) beginning with a subtraction binary operation.

grabbed fourth place and $25,000 with his algebra project on how to partition so-called

Abelian groups into subgroups.

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.

The first edition, published in 1998, was intended as a self-contained work with a focus on structure theory rather than on representation theory or abstract harmonic analysis, although those topics were addressed; also included was such material as an introduction to linear Lie groups, abstract

abelian groups, and category theory.

Consider the composite isomorphism of

abelian groupsToyoda established a connection between medial quasigroups and

Abelian groups (Theorem 2.

He proceeds from the elementary theory of Fourier series and Fourier integrals to abstract harmonic analysis on locally compact

abelian groups.

Note that this includes the class of all finite

abelian groups, because, if G is abelian of order g and H is a subgroup of order h, then [Gamma](G, H) is disconnected with exactly h components each component being complete with g/h vertices.

Fuchs: Infinite

Abelian Groups II, Mir, Moskva, 1977 (in Russian).

The construction of this abelization is expressed in terms of category theory and as in the classical case of

abelian groups it creates a functor called reflector.