  The aim of this work is to study the properties of groups of operators for
evolution equations of quantum many-particle systems, namely, the von Neumann
hierarchy for correlation operators, the BBGKY hierarchy for marginal density
operators and the dual BBGKY hierarchy for marginal observables. We show that
the concept of cumulants (semi-invariants) of groups of operators for the von
Neumann equations forms the basis of the expansions for one-parametric families
of operators for evolution equations of infinitely many particles.
