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For N> 3 there are S_N and D_N actions on the space of solutions of the first nontrivial equation in the SL(N) MKdV hierarchy, generalizing the two Z_2 actions on the space of solutions of the standard MKdV equation. These actions survive scaling reduction, and give rise to transformation groups for certain (systems of) ODEs, including the second, fourth and fifth Painlevé equations.doi:10.1088/0951-7715/7/1/015 fatcat:awxpu5mt4ne2dmwj2nieccheha