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We perform the symmetry analysis of the properties of the ground state of afinite system of interacting spinless bosons for the three most symmetricboundary conditions (BCs): zero BCs with spherical and circular symmetries, aswell as periodic BCs. The symmetry of the system can lead to interestingproperties. For instance, the density of a periodic Bose system is an exactconstant: $\rho(\textbf{r})=const$. Moreover, under the perfect sphericalsymmetry of BCs, the crystalline state cannot produce the Bragg peaks. The mainresult of the article is that symmetry properties and generalquantum-mechanical theorems admit equally both crystalline and liquid groundstate for a Bose system of any density.

Symmetry properties of the ground state of the system of interacting spinless bosons