Abstract The main result of this paper states that fully inert subgroups of torsion-complete abelian p-groups are commensurable with fully invariant subgroups, which have a satisfactory characterization by a classical result by Kaplansky. As the proof of this fact relies on the analogous result for direct sums of cyclic p-groups, we provide revisited and simplified proofs of the fact that fully inert subgroups of direct sums of cyclic p-groups are commensurable with fully invariant subgroups.

中文翻译：

---

扭转完全 p 群的完全惰性子群

摘要 本文的主要结果表明，扭转完全阿贝尔 p 群的完全惰性子群与完全不变子群是可公度的，卡普兰斯基的经典结果具有令人满意的表征。由于这一事实的证明依赖于循环 p-群的直接和的类似结果，我们提供了以下事实的重新审视和简化的证明，即循环 p-群的直接和的完全惰性子群与完全不变子群相称。