Let group generators having finite-dimensional representation be realized as Hermitian linear differential operators without inhomogeneous terms as takes place, for example, for the SO(n) group. Then corresponding group Hamiltonians containing terms linear in generators (along with quadratic ones) give rise to quasi-exactly solvable models with a magnetic field in a curved space. In particular, for the SO(4) group Hamiltonian with isotropic quadratic part, the manifold within which a quantum particle moves has the geometry of the Einstein universe.