  We present two results regarding the three-dimensional Vlasov--Poisson system
in the full space with an external magnetic field. First, we investigate the
propagation of velocity moments for solutions to the system when the magnetic
field is uniform and time-dependent. We combine the classical moment approach
with an induction procedure depending on the cyclotron period
$T_c=||B||_{\infty}^{-1}$. This allows us to obtain, like in the unmagnetized
case, the propagation of velocity moments of order $k>2$ in the full space case
and of order $k>3$ in the periodic case. Second, this time taking a general
magnetic field that depends on both time and position, we manage to extend a
result by Miot arXiv:1409.6988v1 [math.AP] regarding uniqueness for
Vlasov--Poisson to the magnetized framework.
