  In this paper, we study the group Pext(C,A) for locally compact abelian (LCA)
groups A and C. Sufficient conditions are established for Pext(C,A) to coincide
with the first Ulm subgroup of Ext(C,A). Some structural information on pure
injectives in the category of LCA groups is obtained. Letting K denote the
class of LCA groups which can be written as the topological direct sum of a
compactly generated group and a discrete group, we determine the groups G in K
which are pure injective in the category of LCA groups. Finally we describe
those groups G in K such that every pure extension of G by a group in K splits
and obtain a corresponding dual result.
