Generalized Cotorsion Locally Compact Abelian Groups

Abstract

This paper is concerned with the generalization of the concept of cotorsion abelian group. A locally compact abelian group $L$ is called generalized cotorsion if $L$ contains a compact open subgroup $K$ such that the character group of $K$ and the group $L/K$ are cotorsion groups. Some properties and homological characteristics of generalized cotorsion groups are obtained. The classification problem of generalized cotorsion groups is discussed.