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Our studies of solid solutions Pb z Sn 1-z Te doped with In have concentrated on checking for a superconducting transition in the temperature variation of both the resistivity and the magnetization and of an influence on that behaviour of an applied magnetic field. The magnetization of the samples was measured in a SQUID magnetometer using a small field (15 Oe) cooling method. We obtained the dependences of the superconducting critical parameters as a function of the In concentration and the content of isovalent lead. The data for superconductivity correlate with normal state properties and with an influence of the matrix composition on the energy band position of the In states. We observed an enhancement of superconductivity when the Fermi level pinned by the In impurity band enters the heavy hole Σ-band.