Abstract.
A subgroup H of an Abelian group G is said to be fully inert if the quotient 
is finite for every endomorphism ϕ of G.
Clearly, this is a common generalization of the notions of fully invariant, finite and finite-index subgroups. We investigate the fully inert subgroups of divisible Abelian groups, and in particular, those Abelian groups that are fully inert in their divisible hull, called inert groups. We prove that the inert torsion-free groups coincide with the completely decomposable homogeneous groups of finite rank and we give a complete description of the inert groups in the general case. This yields a characterization of the fully inert subgroups of divisible Abelian groups.
Received: 2012-07-18
Revised: 2013-03-04
Published Online: 2013-05-15
Published in Print: 2013-11-01
© 2013 by Walter de Gruyter Berlin Boston
