The purpose of this paper is to prove the following result. Let $\xi _1 ,\xi _2 , \cdots ,\xi _n , \cdots $ be an arbitrary sequence of independent random variables on a locally compact group G. We construct the compositions \[ \xi _n = \xi _1 \xi _2 \cdots \xi _n . \] If elements $a_n \in G$ can be found so that the sequence of normalized compositions \[ \eta _n = \zeta _n a_n \] as a limiting distribution, then the group G is compact.