  We perform the symmetry analysis of the properties of the ground state of a
finite system of interacting spinless bosons for the three most symmetric
boundary conditions (BCs): zero BCs with spherical and circular symmetries, as
well as periodic BCs. The symmetry of the system can lead to interesting
properties. For instance, the density of a periodic Bose system is an exact
constant: $\rho(\textbf{r})=const$. Moreover, under the perfect spherical
symmetry of BCs, the crystalline state cannot produce the Bragg peaks. The main
result of the article is that symmetry properties and general
quantum-mechanical theorems admit equally both crystalline and liquid ground
state for a Bose system of any density.
