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A submodule $W$ of a $p$ -primary module $M$ of bounded order is known to be regular if $W$ and $M$ have simultaneous bases. In this paper we derive necessary and sufficient conditions for regularity of a submodule.

Regularität in torsionsfreien abelschen Gruppen

Edgar Müller, Otto Mutzbauer (1992)

Czechoslovak Mathematical Journal

Regulierende Untergruppen und der Regulator fast vollständig zerlegbarer Gruppen

Bernhard Frey, Otto Mutzbauer (1992)

Rendiconti del Seminario Matematico della Università di Padova

Relatively coarse sequential convergence

Roman Frič, Fabio Zanolin (1997)

Czechoslovak Mathematical Journal

We generalize the notion of a coarse sequential convergence compatible with an algebraic structure to a coarse one in a given class of convergences. In particular, we investigate coarseness in the class of all compatible convergences (with unique limits) the restriction of which to a given subset is fixed. We characterize such convergences and study relative coarseness in connection with extensions and completions of groups and rings. E.g., we show that: (i) each relatively coarse dense group precompletion...

Remarks on duality for $Σ$ -groups. I. Products and coproducts

Denis Higgs (1989)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Remarks on factorizations in algebraic number fields

Jan Śliwa (1982)

Colloquium Mathematicae

Representation of finite abelian group elements by subsequence sums

David J. Grynkiewicz, Luz E. Marchan, Oscar Ordaz (2009)

Journal de Théorie des Nombres de Bordeaux

Let $G ≅ C_{n_{1}} \oplus ... \oplus C_{n_{r}}$ be a finite and nontrivial abelian group with $n_{1} | n_{2} | ... | n_{r}$ . A conjecture of Hamidoune says that if $W = w_{1} \cdot ... \cdot w_{n}$ is a sequence of integers, all but at most one relatively prime to $| G |$ , and $S$ is a sequence over $G$ with $| S | \geq | W | + | G | - 1 \geq | G | + 1$ , the maximum multiplicity of $S$ at most $| W |$ , and $σ (W) \equiv 0 mod | G |$ , then there exists a nontrivial subgroup $H$ such that every element $g \in H$ can be represented as a weighted subsequence sum of the form $g = \underset{i = 1}{\sum^{n}} w_{i} s_{i}$ , with $s_{1} \cdot ... \cdot s_{n}$ a subsequence of $S$ . We give two examples showing this does not hold in general, and characterize the counterexamples...

Representation Type of Posets and Finite Rank Butler Groups

D. Arnold, M. Dugas (1998)

Colloquium Mathematicae

Residually finite groups with the same finite images

Gilbert Baumslag (1974)

Compositio Mathematica

Restricted set addition in Abelian groups: results and conjectures

Vsevolod F. Lev (2005)

Journal de Théorie des Nombres de Bordeaux

We present a system of interrelated conjectures which can be considered as restricted addition counterparts of classical theorems due to Kneser, Kemperman, and Scherk. Connections with the theorem of Cauchy-Davenport, conjecture of Erdős-Heilbronn, and polynomial method of Alon-Nathanson-Ruzsa are discussed.The paper assumes no expertise from the reader and can serve as an introduction to the subject.

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Displaying 1 – 18 of 18

Rational Functions Invariant under a Finite Abelian Group.

Realization theorems for valuated $p^{n}$ -socles

Rearrangements of the Symmetric Group and Enumerative Properties of the Tangent and Secant Numbers.

RECOGNIZABLE LANGUAGES AND FINITE SEMILATTICES OF GROUPS.

Regular submodules of torsion modules over a discrete valuation domain