THE FULLY INVARIANT EXTENDING PROPERTY FOR ABELIAN GROUPS

Abstract

An abelian group has the FI-extending property if every fully invariant subgroup is essential in a direct summand. A mixed abelian group has the FI-extending property if and only if it is a direct sum of a torsion and a torsion-free abelian group, both with the FI-extending property. A full characterization is obtained for the abelian groups with the FI-extending property which are either torsion-free of finite rank or torsion.