  The band structure and magnetotransport of a two-dimensional electron gas
(2DEG), in the presence of the Rashba (RSOI) and Dresselhaus (DSOI) terms of
the spin-orbit interaction and of a perpendicular magnetic field, is
investigated. Exact and approximate analytical expressions for the band
structure are obtained and used to calculate the density of states (DOS) and
the longitudinal magnetoresitivity assuming a Gaussian type of level
broadening. The interplay between the Zeeman coupling and the two terms of the
SOI is discussed. If the strengths $\alpha$ and $ \beta$, of the RSOI and DSOI,
respectively, are equal and the $g$ factor vanishes, the two spin states are
degenerate and a shifted Landau-level structure appears. With the increase of
the difference $\alpha- \beta$, a novel beating pattern of the DOS and of the
Shubnikov-de Haas (SdH) oscillations appears distinctly different from that
occurring when one of these strengths vanishes.
