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This artical concerns the C^1,α_ loc -regularity of weak solutions u to the degenerate subelliptic p-Laplacian equation Δ_H,pu(x)=_i=1^6X_i^*(| abla_H u|^p-2X_iu)=0,where H is the orthogonal complement of a Cartan subalgebra in SU(3) with the orthonormal basis composed of the vector fields X_1,...,X_6. When 1, number=4, journal=Journal of Partial Differential Equations, year=2024, month=Dec., pages=427–466