Standard homological methods and a theorem of Harrison on cotorsion groups are used to prove the result mentioned.
In this note Z denotes an infinite cyclic group, Q the additive group of rational numbers, Zp ∞ a p–quasicyclie group, and Ip the group of p–adic integers.
Pascual Llorente proves in  that Ext(Q,z) is an uncountable group, and gives explicitly a countably infinite subset. Very little extra effort produces the result embodied in the title, as follows.
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