On the fundamental group of the Sierpiński-gasket

We give a description of the fundamental group π(△) of the Sierpiński-gasket △. It turns out that this group is isomorphic to a certain subgroup of an inverse limit formed by the fundamental groups Gn of natural approximations of △. This subgroup, and with it π(△), can be described in terms of sequences of words contained in an inverse limit of semigroups.