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.
We prove that pure subgroups of thick Abelian -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.
It is shown, under ZFC, that a -group has the interesting property of being -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 -groups.
A simple proof is given of a well-known result of the existance of lattice-isomorphisms between locally nilpotent quaternionfree modular groups and abelian groups.
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.
Generalizing the notion of the almost free group we introduce almost Butler groups. An almost -group of singular cardinality is a -group. Since almost -groups have preseparative chains, the same result in regular cardinality holds under the additional hypothesis that is a -group. Some other results characterizing -groups within the classes of almost -groups and almost -groups are obtained. A theorem of stating that a group of weakly compact cardinality having a -filtration consisting...