We report the magnetogyrotropic photogalvanic effect (MPGE) in n-doped (110)-grown GaAs/AlGaAs quantum-well (QW) structures caused by free-carrier absorption of terahertz radiation in the presence of a magnetic field. The photocurrent behavior upon variation in the radiation-polarization state, magnetic field orientation, and temperature is studied. The developed theory of MPGE describes well all experimental results. It is demonstrated that the structure inversion asymmetry can be controllably tuned to zero by variation in the delta-doping layer positions. For the in-plane magnetic field the photocurrent is only observed in asymmetric structures but vanishes in symmetrically doped QWs. Applying time-resolved Kerr rotation and polarized luminescence we investigate the spin relaxation in QWs for various excitation levels. Our data confirm that in symmetrically doped QWs the spin-relaxation time is maximal; therefore, these structures set the upper limit of spin dephasing in GaAs/AlGaAs QWs.</p>.