  We performed magnetic and ferroelectric measurements, associated with Landau
theory and symmetry analysis, in order to clarify the situation of the YMnO3
system, a classical example of type I multiferroics. We found that the only
magnetic group compatible with all experimental data (neutrons scattering,
magnetization,polarization, dielectric constant, second harmonic generation) is
the P6'3 group. In this group a small ferromagnetic component along c is
induced by the Dzyaloshinskii-Moriya interaction, and observed here in SQUID
magnetization measurements. We found that the ferromagnetic and
antiferromagnetic components can only be switched simultaneously, while the
magnetic orders are functions of the polarization square and therefore
insensitive to its sign.
