Group properties of equations of the kinetic theory of coagulation

Nonlocal equations of the coagulation theory are studied by methods of group analysis. In addition to the integrodifferential Smoluchowski equation, equivalent models are also considered, including the equation for the Laplace transform of the original equation, an infinite system of equations for the power moments of its solution, and the equation for the generating function of the power moments. Admissible Lie groups for the considered equations are found, their relationships are studied, and the corresponding invariant solutions are analyzed.