  Higman proved in 1952 that every free group is non-commutatively slender,
this is to say that if G is a free group and h is a homomorphism from the
countable complete free product (X_omega Z) to G, then there exists a finite
subset F of omega and a homomorphism h:*_{i in F} Z --> G such that h=h rho_F,
where rho_F is the natural map from (X_{i in omega})Z to *_{i in F}Z .
Corresponding to the abelian case this phenomenon was called the
non-commutative Specker Phenomenon. In this paper we show that Higman's result
fails if one passes from countable to uncountable. In particular, we show that
for non-trivial groups G_alpha (alpha in lambda) and uncountable cardinal
lambda there are 2^{2^lambda} homomorphisms from the complete free product of
the G_alpha 's to the ring of integers.
