This paper is devoted to identification of the most important factors responsible for formation of magnetic moments at edges of graphene-like nanoribbons. The main role is attributed to the Hubbard correlations (within unrestricted Hartree-Pock approximation) and intrinsic spin orbit interactions, but additionally a perpendicular electric field is also taken into account. Of particular interest is the interplay of the in-plane edge magnetism and the energy band gap. It is shown that, with the increasing electric field, typically the following phases develop: magnetic insulator (with in-plane spins). nomnagnetic narrow-band semiconductor, and nonmagnetic band insulator.