The present paper is devoted to the group classification of magnetogasdynamics equations in which dependent variables in Euler coordinates depend on time and two spatial coordinates. It is assumed that the continuum is inviscid and nonthermal polytropic gas with infinite electrical conductivity. The equations are considered in mass Lagrangian coordinates. Use of Lagrangian coordinates allows reducing number of dependent variables. The analysis presented in this article gives complete group classification of the studied equations. This analysis is necessary for constructing invariant solutions and conservation laws on the base of Noether’s theorem.

Recently, an infinitesimal approach for finding reciprocal transformations has been proposed. The method uses the group analysis approach and consists of similar steps as for finding an equivalence group of transformations. The new method provides a systematic tool for finding classes of reciprocal transformations (group of reciprocal transformations). Similar to the classical group analysis this approach can be also applied for finding all reciprocal transformations (not only composing a group) of the equations under study. The present paper provides this algorithm. As an illustration, the method is applied to the two-dimensional stationary gas dynamics equations. Equivalence group, group of reciprocal transformations and completeness of all discrete reciprocal transformations are presented in the paper. The results are stated in form of a theorem.