2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115024An exact approach for the factorization of the relativistic linear singular oscillator is proposed. This model is expressed by the finite-difference Schrödinger-like equation. We have found finite-difference raising and lowering operators, which are with the Hamiltonian operator form the close Lie algebra of the $SU(1, 1)$ group.7 pages, EPL style LaTeX file, accepted for publication in Europhysics LettersMathematical Physics39A05; 22E45; 22E70text