  Let A be a basic connected finite dimensional algebra over a field k and let
Q be the ordinary quiver of A. To any presentation of A with Q and admissible
relations, R. Martinez-Villa and J. A. de La Pena have associated a group
called the fundamental group of this presentation. There may exist different
presentations of A with non isomorphic fundamental groups. In this note, we
show that if the field k has characteristic zero, if Q has no oriented cycles
and if Q has no double bypasses then there exists a privileged presentation of
A such that the fundamental group of any other presentation is the quotient of
the fundamental group of this privileged presentation.
