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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...

Very Decomposable Abelian Groups.

Martin Ziegler, Rüdiger Göbel (1988/1989)

Mathematische Zeitschrift

Warfield Invariants in Abelian Group Algebras

Peter Danchev (2008)

Collectanea Mathematica

Warfield invariants in abelian group rings.

Peter V. Danchev (2005)

Extracta Mathematicae

Let R be a perfect commutative unital ring without zero divisors of char(R) = p and let G be a multiplicative abelian group. Then the Warfield p-invariants of the normed unit group V (RG) are computed only in terms of R and G. These cardinal-to-ordinal functions, combined with the Ulm-Kaplansky p-invariants, completely determine the structure of V (RG) whenever G is a Warfield p-mixed group.

Weighted sequences in finite cyclic groups.

Grynkiewicz, David J., Zhuang, Jujuan (2009)

Applied Mathematics E-Notes [electronic only]

When the intrinsic algebraic entropy is not really intrinsic

Brendan Goldsmith, Luigi Salce (2015)

Topological Algebra and its Applications

The intrinsic algebraic entropy ent(ɸ) of an endomorphism ɸ of an Abelian group G can be computed using fully inert subgroups of ɸ-invariant sections of G, instead of the whole family of ɸ-inert subgroups. For a class of groups containing the groups of finite rank, aswell as those groupswhich are trajectories of finitely generated subgroups, it is proved that only fully inert subgroups of the group itself are needed to comput ent(ɸ). Examples show how the situation may be quite different outside...

We show that in a cyclic group with $n$ elements every zero-sumfree sequence $S$ with length $| S | \geq \frac{n + 1}{2}$ contains some element of order $n$ with high multiplicity.