  A composite quantum system comprising a finite number k of subsystems which
are described with position and momentum variables in Z_{n_{i}}, i=1,...,k, is
considered. Its Hilbert space is given by a k-fold tensor product of Hilbert
spaces of dimensions n_{1},...,n_{k}. Symmetry group of the respective finite
Heisenberg group is given by the quotient group of certain normalizer. This
paper extends our previous investigation of bipartite quantum systems to
arbitrary multipartite systems of the above type. It provides detailed
description of the normalizers and the corresponding symmetry groups. The new
class of symmetry groups represents a very specific generalization of
symplectic groups over modular rings. As an application, a new proof of
existence of the maximal set of mutually unbiased bases in Hilbert spaces of
prime power dimensions is provided.
