[en] The reduced probabilities of M2-transitions between the low-lying states 11/2^-₁ and 7/2₁⁺ in Sn, Sb, Pr, Pm and Eu isotopes and 15/2₁^- and 11/2₁⁺-states in sup(209)Pb are calculated within the quasiparticle-phonon nuclear model. The M2-polarization of the even-even core reduces the B(M2)-values by 3-4 times as compared with the single-particle limit. The core polarization effect is strongest when the isoscalar spin-dipole interaction vanishes. In spite of this strong reduction B(M2)sub(theor) are still by 4-5 times larger than the experimantal values of B(M2) in all the nuclei under considreration except for sup(209)Pb. So, it is necessary to use too small values of effective spin gyromagnetic factors (gsub(e)sup(eff) approximately 0.5gsub(s)sup(free)). In sup(209)Pb theory and experiment are in agreement at the usual values of gsub(s)sup(eff) approximately 0.8gsub(s)sup(free)