Abstract
We consider a subclass of Butler groups, the OB (2) -groups. The class B (2) consists of the groups G which appear in an exact sequence 0 → K → D → G → 0 where D is a finite rank completely decomposable group and K is a rank two pure subgroup of D . The groups G belonging to OB (2)⊆ B (2) satisfy an additional condition called “overlap”. We discuss three questions: (1) When is G strongly indecomposable? (2) To what extent is D determined by G ? (3) Is there a reasonable set of numerical invariants for such a G ? We find definitive answers for these questions in the case of strongly indecomposable balanced OB (2)-groups. We also obtain partial results without the balanced hypothesis.
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