Abstract:
The following questions are discussed: 1) what is the maximum possible complexity of a
finite-dimensional group $\mathscr{G}$ of “latent” symmetry? 2) does the existence of a complete set
of single-valued integrals of motion always imply the existence of a nontrivial group $\mathscr{G}$?
The impossibility of essential extension of the groups $\mathscr{G}$ for known examples is proved; a
negative answer is given to the second question.
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