Abstract
In this paper, we study the time variable coefficient modified Korteweg-de Vries (mKdV) equation from group-theoretic point of view. We obtain Lie point symmetries admitted by the mKdV equation for various forms for the time variable coefficients. We use the symmetries to construct the group-invariant solutions for each of the cases of the arbitrary variable coefficients. Finally, the solitary wave ansatz will be used to carry out the integration of the mKdV equation that will be supported by a concrete example.