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(1,4)-groups with homocyclic regulator quotient of exponent p³

David M. Arnold, Adolf Mader, Otto Mutzbauer, Ebru Solak (2015)

Colloquium Mathematicae

The class of almost completely decomposable groups with a critical typeset of type (1,4) and a homocyclic regulator quotient of exponent p³ is shown to be of bounded representation type. There are precisely four near-isomorphism classes of indecomposables, all of rank 6.

A note on a theorem of Megibben

Peter Vassilev Danchev, Patrick Keef (2008)

Archivum Mathematicum

We prove that pure subgroups of thick Abelian p -groups which are modulo countable are again thick. This generalizes a result due to Megibben (Michigan Math. J. 1966). Some related results are also established.

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 result on B 1 -groups

Ladislav Bican, K. M. Rangaswamy (1995)

Rendiconti del Seminario Matematico della Università di Padova

Abelian groups have/are near Frattini subgroups

Simion Breaz, Grigore Călugăreanu (2002)

Commentationes Mathematicae Universitatis Carolinae

The notions of nearly-maximal and near Frattini subgroups considered by J.B. Riles in [20] and the natural related notions are characterized for abelian groups.

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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