Recently, Raimund Preusser displayed very short polynomial expressions of elementary generatorsin classical groups over an arbitrary commutative ring as products of conjugates of an arbitrarymatrix and its inverse by absolute elementary matrices. In particular, this provides very shortproofs for description of normal subgroups. In 2018, the author discussed various generalizationsof these results to exceptional groups, specifically those of types E6and E7. Here, a furthervariation of Preusser’s wonderful idea is presented. Namely, in the case of GL(n, R), n ≥ 4 ,similar expressions of elementary transvections as conjugates of g ∈ GL(n, R) and g−1by relativeelementary matrices x ∈ E(n, J) and then x ∈ E(n, R, J), for an ideal J R, are obtained. Again,in particular, this allows to give very short proofs for the description of subgroups normalized byE(n, J) or E(n, R, J), and thus also of subnormal subgroups in GL(n, R).