  Increased interest in physics of graphene and other two-dimensional materials
boosted investigations of band structure near nodal points and lines. In
contrast, group theoretical explanation of simple bands (that do not touch
other bands), is sporadically present in the literature. This paper presents
electronic dispersions up to forth order in momentum, near Brillouin zone (BZ)
high symmetry points of all eighty layer groups. The method applies to non
magnetic materials both with or without spin-orbit coupling. Particular
attention is devoted to Mexican-hat dispersion, showing that it can appear only
at BZ center of hexagonal layer groups. Presented symmetry adapted Taylor
expansion of bands can be used to fit ab-initio or experimental band
structures, or for analytical calculation of crystal properties. The results
presented here might serve also as a guiding tool for design of new
two-dimensional materials.
