Indecomposable p-Local Torsion-Free Groups with Quadratic and Cubic Splitting Fields

Abstract

Indecomposable torsion-free p-local Abelian groups of finite rank with quadratic and cubic splitting field K are characterized. As a consequence, for groups with quadratic splitting field K it is proved that K-decomposable p-local torsion-free Abelian groups of finite rank are isomorphic if and only if their endomorphism rings are isomorphic.