  The formation and dynamics of full vortex gap solitons (FVGSs) is
investigated in two-component Bose-Einstein condensates with spin-orbit
coupling (SOC), Zeeman splitting (ZS), and competing cubic and quintic
nonlinear terms, while the usual kinetic energy is neglected, assuming that it
is much smaller than the SOC and ZS terms. Unlike previous SOC system with the
cubic-only attractive nonlinearity, in which solely semi-vortices may be
stable, with the vorticity carried by a single component, the present system
supports stable FVGS states, with the vorticity present in both components
(such states are called here full vortex solitons, to stress the difference
from the half-vortices). They populate the bandgap in the system's linear
spectrum. In the case of the cubic self-attraction and quintic repulsion,
stable FVGSs with a positive effective mass exist near the top of the bandgap.
On the contrary, the system with cubic self-repulsion and quintic attraction
produces stable FVGSs with a negative mass near the bottom of the bandgap.
Mobility and collisions of FVGSs with different topological charges are
investigated too.
