turkmath.org

A torsion free abelian group of finite rank is called almost completely decomposable if it has a completely decomposable subgroup of finite index. We consider classes of p-reduced almost completely decomposable groups with a (finite) p-group as regulator quotient, and an inverted forest as critical typeset. A preduced almost completely decomposable group with regulator quotient a finite p-group is associated to an integer coordinate matrix. A p-local, p-reduced almost completely decomposable group of type (1, 3) is called a (1, 3)-group. It is possible to determine the near-isomorphism classes of indecomposable (1, 3)-groups by using coordinate matrices.