TY - JOUR
T1 - Fully inert subgroups of divisible Abelian groups
AU - Dikranjan, Dikran
AU - Bruno, Anna Giordano
AU - Salce, Luigi
AU - Virili, Simone
PY - 2013/11/1
Y1 - 2013/11/1
N2 - A subgroup H of an Abelian group G is said to be fully inert if the quotient (H + ø(H))/H is finite for every endomorphism ø 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. © de Gruyter 2013.
AB - A subgroup H of an Abelian group G is said to be fully inert if the quotient (H + ø(H))/H is finite for every endomorphism ø 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. © de Gruyter 2013.
U2 - 10.1515/jgt-2013-0014
DO - 10.1515/jgt-2013-0014
M3 - Article
VL - 16
SP - 915
EP - 939
JO - Journal of Group Theory
JF - Journal of Group Theory
SN - 1433-5883
IS - 6
ER -