  Group theory analysis for two-dimensional elemental systems related to
phosphorene is presented, including (i) graphene, silicene, germanene and
stanene, (ii) dependence on the number of layers and (iii) two stacking
arrangements. Departing from the most symmetric $D_{6h}^{1}$ graphene space
group, the structures are found to have a group-subgroup relation, and analysis
of the irreducible representations of their lattice vibrations makes it
possible to distinguish between the different allotropes. The analysis can be
used to study the effect of strain, to understand structural phase transitions,
to characterize the number of layers, crystallographic orientation and
nonlinear phenomena.
