On isomorphism of minimal direct summands

Abstract

Let $G$ be a quasi-complete p-group and let $A$ be a subgroup of $G$ such that there exists a direct summand $L$ of $G$ containing $A$ which is minimal among the direct summands of $G$ that contain $A$. Such a direct summand $L$ is said to be a minimal direct summand of $G$ containing $A$. We prove that all minimal direct summands of G containing $A$ are isomorphic.