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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

AE-rings

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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