“…In this paper, we will determine the condition to construct epimorphisms between finite symmetric mpM -algebras, with the purpose of computing them. To know how the epimorphisms can be built, it is useful, for instance, to determine the lattice of subvarieties of the variety of symmetric mpM -algebras, see [12,Section 7]. Furthermore, the construction of epimorphisms between two finite algebra can be used to compute the cardinality of free algebras in finite generated varieties as it was the case of [12,Section 6].…”