It is shown that the extension functor defined on the category ' of locally compact abelian groups is right-exact. Actually Extn is shown to be zero for all n ?2. Various applications are obtained which deal with the general problem as to when a locally compact abelian group is the direct product of a connected group and a totally disconnected group. One such result is that a locally compact abelian group G has the property that every extension of G by a connected group in ' splits iff G = (R/Z)A G Rn for some cardinal a and positive integer n. 1. In a previous paper [3] we set up the homological theory needed for the development of an extension functor Ext for the category Y of locally compact abelian groups. In that paper some of the properties of Ext were discovered and various applications were found. It was shown that Ext preserves exactness except possibly at the right end of the usual long exact sequence connecting Hom and Ext. In this paper we show that Ext is right-exact and in fact that Extn = 0 for n > 2. Also further applications are found relating to the general problem as to when a locally compact abelian group splits into the direct product of a connected group and a totally disconnected one. We refer the reader to [3] for pertinent comments regarding the historical development of our subject. Also see [3] regarding notation and terminology. 2. The functor Ext is right-exact. Our first theorem proves to be a useful reduction theorem. In some instances, it may be used to show that it is sufficient to work with compactly generated groups. THEOREM 2.1. Suppose that +: G -H is a proper epimorphism in Y and that H is compactly generated. Then there is a compactly generated subgroup L of G such that +(L) = H. Moreover, L can be chosen so that GIL is discrete. Proof. By Theorem 24.30 of Hewitt and Ross [5], G=M G0 Rn where M contains some compact open subgroup B. Since B ?) Rn is open in G, O(B (E Rn) is Presented to the Society, January 24, 1969; received by the editors October 9, 1968 and, in revised form, March 20, 1970. AMS 1968 subject classifications. Primary 2220; Secondary 2210.