  The Milnor number of an isolated hypersurface singularity, defined as the
codimension $\mu(f)$ of the ideal generated by the partial derivatives of a
power series $f$ that represents locally the hypersurface, is an important
topological invariant of the singularity over the complex numbers. However it
may loose its significance when the base field is arbitrary. It turns out that
if the ground field is of positive characteristic, this number depends upon the
equation $f$ representing the hypersurface, hence it is not an invariant of the
hypersurface. For a plane branch represented by an irreducible convergent power
series $f$ in two indeterminates over the complex numbers, it was shown by
Milnor that $\mu(f)$ always coincides with the conductor $c(f)$ of the
semigroup of values $S(f)$ of the branch. This is not true anymore if the
characteristic of the ground field is positive. In this paper we show that,
over algebraically closed fields of arbitrary characteristic, this is true,
provided that the semigroup $S(f)$ is tame, that is, the characteristic of the
field does not divide any of its minimal generators.
