We discuss the possibility of obtaining a non-abelian discrete flavor
symmetry from an underlying continuous, possibly gauged, flavor symmetry SU(2)
or SU(3) through spontaneous symmetry breaking. We consider all possible cases,
where the continuous symmetry is broken by small representations. "Small"
representations are these which couple at leading order to the Standard Model
fermions transforming as two- or three-dimensional representations of the
flavor group. We find that, given this limited representation content, the only
non-abelian discrete group which can arise as a residual symmetry is the
quaternion group D_2'.Comment: 15 page
