On the Abelian extensions of locally compact Abelian groups

The group of all Abelian extensions of a compact Abelian group by a discrete Abelian group is calculated completely. Criteria are found for the vanishing of the group of all Abelian extensions of a discrete Abelian group by a compact one. Two criteria for the splitting of compact Abelian groups are obtained. The question is studied of conditions for the vanishing of the group of all Abelian extensions of a totally disconnected locally compact Abelian group by an arbitrary locally compact Abelian group.
Bibliography: 10 titles.