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A characterization of Ext(G,ℤ) assuming (V = L)

Saharon Shelah, Lutz Strüngmann (2007)

Fundamenta Mathematicae

We complete the characterization of Ext(G,ℤ) for any torsion-free abelian group G assuming Gödel’s axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence ( ν p : p Π ) of cardinals satisfying ν p 2 ν (where Π is the set of all primes), there is a torsion-free abelian group G of size ν such that ν p equals the p-rank of Ext(G,ℤ) for every...

A property of B 2 -groups

Kulumani M. Rangaswamy (1994)

Commentationes Mathematicae Universitatis Carolinae

It is shown, under ZFC, that a B 2 -group has the interesting property of being 0 -prebalanced in every torsion-free abelian group in which it is a pure subgroup. As a consequence, we obtain alternate proofs of some well-known theorems on B 2 -groups.

A remark on hyper-indecomposable groups

Ladislav Bican (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Un gruppo abeliano senza torsione ed indecomponibile è detto iperindecomponibile se tutti i sottogruppi propri del suo inviluppo iniettivo che lo contengono sono indecomponibili. In questo lavoro si caratterizza la classe dei gruppi iperindecomponibili per mezzo di loro proprietà locali. I gruppi iperindecomponibili omogenei sono caratterizzati tramite la proprietà «factor-splitting».

A result on B 1 -groups

Ladislav Bican, K. M. Rangaswamy (1995)

Rendiconti del Seminario Matematico della Università di Padova


Manfred Dugas, Shalom Feigelstock (2004)

Rendiconti del Seminario Matematico della Università di Padova

Algebraic ramifications of the common extension problem for group-valued measures

Rüdiger Göbel, R. Shortt (1994)

Fundamenta Mathematicae

Let G be an Abelian group and let μ: A → G and ν: B → G be finitely additive measures (charges) defined on fields A and B of subsets of a set X. It is assumed that μ and ν agree on A ∩ B, i.e. they are consistent. The existence of common extensions of μ and ν is investigated, and conditions on A and B facilitating such extensions are given.

Almost Butler groups

Ladislav Bican (2000)

Czechoslovak Mathematical Journal

Generalizing the notion of the almost free group we introduce almost Butler groups. An almost B 2 -group G of singular cardinality is a B 2 -group. Since almost B 2 -groups have preseparative chains, the same result in regular cardinality holds under the additional hypothesis that G is a B 1 -group. Some other results characterizing B 2 -groups within the classes of almost B 1 -groups and almost B 2 -groups are obtained. A theorem of stating that a group G of weakly compact cardinality λ having a λ -filtration consisting...

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