[en] A possible construction of the SU(6) algebra in the fermion Fock space has been discussed. It is argued that in order to find a microscopic justification of the Ineracting Boson Model one should construct the fermion-number-conserving shift operator F-circumflex_μ⁺, playing in the fermion SU(6) algebra a role analogous to the d_μ⁺s generator of the boson realization of SU(6) and that the boson operators itself need not to have a microscopic significance. It is shown however that such shift operator cannot be a single-particle operator. An example of a non-single-particle SU(6) shift operator is provided by the Ginocchio model but a closed algebraic form of it is difficult to unveil. 12 refs., 1 fig., 1 tab. (author)