Locally Compact Abelian p-Groups Revisited

Abstract

Even though the structure of locally compact abelian groups is generally considered to be rather thoroughly known through a wealth of publications, one keeps encountering corners that are not elucidated in up-to-date literature. In a study of a particular class of metabelian locally compact groups (see [HHR17]) we encountered some issues about noncompact locally compact abelian groups which do not appear to be discussed in the literature even though some of them were anticipated in Braconnier's article on his local product [Bra48]. Here we treat some of them, notably some aspects of totally disconnected torsion-free locally compact abelian groups which one might consider unexpected if not pathological. However, firstly we deal with some points concerning noncompact locally compact abelian torsion groups. For compact abelian groups we often refer to the monograph [HM13]. It will be convenient to use additive notation for abelian groups.