  An infinitary version of the notion of free products has been introduced and
investigated by G.Higman. Let G_i (for i in I) be groups and ast_{i in X} G_i
the free product of G_i (i in X) for X Subset I and p_{XY}: ast_{i in Y}
G_{i}->ast_{i in X} G_{i} the canonical homomorphism for X subseteq Y Subset I.
(X Subset I denotes that X is a finite subset of I.) Then, the unrestricted
free product is the inverse limit lim (ast_{i in X} G_i, p_{XY}: X subseteq Y
Subset I). We remark ast_{i in emptyset} G_i= {e} . We prove:
  Theorem: Let F be a free group. Then, for each homomorphism h:lim ast G_i-> F
there exist countably complete ultrafilters u_0,...,u_m on I such that h = h .
p_{U_0 cup ... cup U_m} for every U_0 in u_0, ...,U_m in u_m. If the
cardinality of the index set I is less than the least measurable cardinal, then
there exists a finite subset X_0 of I and a homomorphism overline {h}: ast_{i
in X_0}G_i-> F such that h= overline {h} . p_{X_0}, where p_{X_0}: lim ast
G_i->ast_{i in X_0}G_i is the canonical projection.
