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.
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 new class of -primary abelian groups that are Hausdorff in the -adic topology and that generalize direct sums of cyclic groups are studied. We call this new class of groups almost coproducts of cyclic groups. These groups are defined in terms of a modified axiom 3 system, and it is observed that such groups appear naturally. For example, is almost a coproduct of finite cyclic groups whenever is a Hausdorff -primary group and is the group of normalized units of the modular group algebra...