Characterization of Symmetry Properties of First Integrals for Submaximal Linearizable Third-Order ODEs

Table 5

The commutation relations for the symmetries of (27).

[𝑋𝑖, 𝑋𝑗]	𝑋1	𝑋2	𝑋3	𝑋4
𝑋1	0	0	0	𝑋1
𝑋2	0	0	0	𝑋2
𝑋3	0	0	0	𝑋3
𝑋4	−𝑋1	−𝑋2	−𝑋3	0