Characterization of the Decomposable Groups and Group Functions

Decomposition of group functions is of considerable importance for the cascade synthesis of multivalued functions. We study cascades satisfying the more restrictive criterion “strongly decomposable”. This approach introduces in a natural way a set of subgroups cGm of G with the property that every m variable function into Gm is decomposable over G. Further, Gm is the maximal subgroup of G with this property. The decomposable subgroups of G are the subgroups of ∩m=1∞Gm.