  We have studied properties and shell structure of the superheavy elements
from Z=102 to Z=120 within the framework of the RMF theory. The region of study
spans nuclides with neutron numbers N=150-190. The Lagrangian model NL-SV1 with
the inclusion of the vector self-coupling of the omega-meson has been employed
in this work. We have performed RMF + BCS calculations for an axially deformed
configuration of nuclei. The ground-state binding energies, single-particle
properties and quadrupole deformation of nuclei have been obtained from the
mean-field minimizations. Two-neutron separation energies, $Q_\alpha$ values
and alpha-decay half-life have been evaluated. It is shown that a large number
of nuclides exhibit the phenomenon of shape-coexistence over a significant
region of the superheavy elements. Shape coexistence of a prolate and an oblate
shape is prevalent in nuclides far below N=184, whilst nuclei in the vicinity
of N=184 tend to show a shape coexistence between a spherical and an oblate
shape. The shell structure and 2-neutron separation energies obtained with the
RMF theory reinforce the neutron number N=184 as a major magic number. It is
shown that the neutron number N=172 acts akin to a magic number in the deformed
region. It is suggested that the combination Z=120 and N=172 has the potential
of being a doubly magic number in the superheavy region.
