Generalized presentations of groups, in particular of $Aut(F_\omega)$

The fundamental group of the Hawaiian Earring is not free. However it behaves like free and it can be used to develop a theory of generalized presentations of groups. We give clear generalized presentatons of any symmetric group and of the automorphism group of the free group of infinite countable rang. This is a joint work with W. Singhof.