  Being motivated by the paper [O. I. Bogoyavlenskij, Phys. Rev. 66, 056410
(2002)] we generalise the symmetry transformations for MHD equilibria with
isotropic pressure and incompressible flow parallel to the magnetic field
introduced therein in the case of respective CGL equilibria with anisotropic
pressure. We find that the geometrical symmetry of the field-aligned equilibria
can break by those transformations only when the magnetic field is purely
poloidal. In this situation we derive three-dimensional CGL equilibria from
given axisymmetric ones. Also, we examine the generic symmetry transformations
for MHD and CGL equilibria with incompressible flow of arbitrary direction,
introduced in a number of papers, and find that they cannot break the
geometrical symmetries of the original equilibria, unless the velocity and
magnetic field are collinear and purely poloidal.
