  Symmetric and k-cyclic structure of modal pseudocomplemented De Morgan
algebras algebras was introduced previously. In this paper, we first present
the construction of epimorphims between finite symmetric (or 2-cyclic) modal
pseudocomplemented De Morgan algebras. Furthermore, we compute the cardinality
of the set of all epimorphism between finite structures. Secondly, we present
the construction of finite free algebras on the variety of k-cyclic modal
pseudocomplemented De Morgan algebras and display how our computations are in
fact generalizations to others in the literature. Our work is strongly based on
the properties of epimorphisms and automorphisms and the fact that the variety
is finitely generated.
