  In this note we prove the claim given in the title. A group G is
noncommutatively slender if each map from the fundamental group of the Hawaiian
Earring to G factors through projection to a canonical free subgroup. Graham
Higman, in his seminal 1952 paper, proved that free groups are noncommutatively
slender. Such groups were first defined by K. Eda. Eda has asked which finitely
presented groups are noncommutatively slender. This result demonstrates that
random finitely presented groups in the few- relator sense of Gromov are
noncommutatively slender.
