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 lim ← G n formed by the fundamental groups G n 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.