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Quantum mechanical systems with position dependent masses (PDM) admitting forand more dimensional symmetry algebras are classified. Namely, all PDM systemsare specified which, in addition to their invariance w.r.t. a three parametricLie group, admit at least one second order integral of motion. The presentedclassification is partially extended to the more generic systems which admitone or two parametric Lie groups.

Superintegrable quantum mechanical systems with position dependent masses invariant with respect to three parametric Lie groups