Primary Abelian Groups Isomorphic to the Proper Fully Invariant Subgroup

Abstract

We study primary Abelian groups containing proper fully invariant subgroup isomorphic to the group. The admissable sequence of the Ulm–Kaplansky invariants for primary groups is used. Using these sequences, IF-groups are described in some important classes of Abelian p-group.

Key Words:

• Fully invariant subgroups
• IF-groups
• Separable groups
• Torsion complete p-groups
• Ulm–Kaplansky invariants

2010 Mathematics Subject Classification:

• Primary 20K10
• Secondary 20K25
• 20K27

Notes

Communicated by A. Olshanskii.