  We answered the old question: does there exist a mechanical system with 3
degrees of freedom, except for the Coulomb system, which has 6 first integrals
generating the Lie algebra o(4) by means of the Poisson brackets? We presented
a system which is not centrally symmetric, but has such 6 first integrals. We
showed also that not every mechanical system with 3 degrees of freedom
possesses such Lie algebra o(4).
