This paper arose from
consideration of the following questions. First, what characterizes those infinite
Abelian reduced p-groups which possess disjoint basic subgroups? Second, are there
properties that a basic subgroup must possess to insure the existence of a basic
subgroup disjoint from it? We show that a necessary and sufficient condition for an
infinite Abelian reduced p-group G to contain disjoint basic subgroups is that
|G|=final rank G. Futhermore, in such a group a necessary and sufficient condition
for a basic subgroup B to have a basic subgroup disjoint from it is that B is a lower
basic subgroup of G.
