  A recent paper considered symmetries and conservation laws of the plane
one-dimensional flows for magnetohydrodynamics in the mass Lagrangian
coordinates. This paper analyses the one-dimensional magnetohydrodynamics flows
with cylindrical symmetry in the mass Lagrangian coordinates. The medium is
assumed inviscid and thermally non-conducting. It is modeled by a polytropic
gas. Symmetries and conservation laws are found. The cases of finite and
infinite electric conductivity need to be analyzed separately. For finite
electric conductivity $\sigma (\rho,p)$ we perform Lie group classification,
which identifies $\sigma (\rho,p)$ cases with additional symmetries. The
conservation laws are found by direct computation. For cases with infinite
electric conductivity variational formulations of the equations are considered.
Lie group classifications are obtained with the entropy treated as an arbitrary
element. A variational formulation allows to use the Noether theorem for
computation of conservation laws. The conservation laws obtained for the
variational equations are also presented in the original (physical) variables.
