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Self-small products of abelian groups

Josef Dvořák, Jan Žemlička (2022)

Commentationes Mathematicae Universitatis Carolinae

Let A and B be two abelian groups. The group A is called B -small if the covariant functor Hom ( A , - ) commutes with all direct sums B ( κ ) and A is self-small provided it is A -small. The paper characterizes self-small products applying developed closure properties of the classes of relatively small groups. As a consequence, self-small products of finitely generated abelian groups are described.

Various local global principles for abelian groups.

George Peschke, Peter Symonds (1994)

Publicacions Matemàtiques

We discuss local global principles for abelian groups by examining the adjoint functor pair obtained by (left adjoint) sending an abelian group A to the local diagram L(A) = {Z(p) ⊗ A → Q ⊗ A} and (right adjoint) applying the inverse limit functor to such diagrams; p runs through all integer primes. We show that the natural map A → lim L(A) is an isomorphism if A has torsion at only finitely many primes. If A is fixed we answer the genus problem of identifying all those groups B for which the local...

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