  It is proposed to use the Lie group theory of symmetries of differential
equations to investigate the system of equations describing a static star in a
radiative and convective equilibrium. It is shown that the action of an
admissible group induces a certain algebraic structure in the set of all
solutions, which can be used to find a family of new solutions. We have
demonstrated that, in the most general case, the equations admit an infinite
parameter group of quasi-homologous transformations. We have found invariants
of the symmetries group which correspond to the fundamental relations
describing a physical characteristic of the stars such as the
Hertzsprung-Russell diagram or the mass-luminosity relation. In this way we can
suggest that group invariants have not only purely mathematical sense, but
their forms are closely associated with the basic empirical relations.
