Ebru Solak

Representations of Posets and Indecomposable Torsion-Free Abelian Groups

Representations of posets in certain modules are used to find indecomposable almost completely decomposable torsion-free abelian groups. For a special class of almost completely decomposable groups we determine the possible ranks of indecomposable groups and show that the possible ranks are realized by indecomposable groups in the class.

The Class of (2, 3)-Groups with Homocyclic Regulator Quotient of Exponent p 2

The class of almost completely decomposable groups with a critical typeset of type (2, 3) and a homocyclic regulator quotient of exponent p2 is shown to be of bounded representation type. There are only 5 near-isomorphism classes of indecomposables and they are of rank 5 or 6.

A Remak-Krull-Schmidt Class of Torsion-Free Abelian Groups

The class of almost completely decomposable groups with a critical typeset of type (1, 5) and a homocyclic regulator quotient of exponent p3 is shown to be of bounded representation type, i.e., in particular, a Remak-Krull-Schmidt class of torsion-free abelian groups. There are precisely 20 near-isomorphism classes of indecomposables all of rank 7, 8, 9.