  A systematic search for the Lie point symmetries admitted by the steady
hydromagnetic two-dimensional incompressible viscous flow boundary layer
equation and associated boundary conditions is performed. Unlike previous
works, the specific forms of the external velocity and transverse magnetic
fields are not postulated from the very beginning. In this way a whole new
class of similarity reductions for the problem is derived, for applied fields
having an exponential nature. The corresponding hydromagnetic Falkner-Skan
equation is numerically solved for different velocity profiles at the wall,
considering stretching, expansion, injection or suction. For intense magnetic
fields a series solution is derived and used to investigate the behaviour of
the skin friction with respect to the initial conditions for both expanding and
converging flows.
