  In the context of discrete flavor symmetries, we elaborate a method that
allows one to obtain relations between the mixing parameters in a
model-independent way. Under very general conditions, we show that flavor
groups of the von Dyck type, that are not necessarily finite, determine the
absolute values of the entries of one column of the mixing matrix. We apply our
formalism to finite subgroups of the infinite von Dyck groups, such as the
modular groups, and find cases that yield an excellent agreement with the best
fit values for the mixing angles. We explore the Klein group as the residual
symmetry of the neutrino sector and explain the permutation property that
appears between the elements of the mixing matrix in this case.
