  It is shown that in the case of multicomponent integrable systems connected
with algebras $A_n$, the discrete transformation $T$ possesses the fine
structure and can be represented in the form $T=\prod T_i^{l_i}$, where $T_i$
are n commuting basis discrete transformations, and $l_i$ are arbitrary natural
numbers. All the calculations are conducted in detail for the case of a 3-wave
interacting system.
