The polarization properties of the elastic electron scattering on H-like ions are investigated within the framework of the relativistic QED theory. The polarization properties are determined by a combination of relativistic effects and spin exchange between the incident and bound electrons. The scattering of a polarized electron on an initially unpolarized ion is fully described by five parameters. We study these parameters for non-resonant scattering, as well as in the vicinity of LL resonances, where scattering occurs through the formation and subsequent decay of intermediate autoionizing states. The study was carried out for ions from $txt{B}^{4+}$ to $txt{Xe}^{53+}$. Special attention was paid to the study of asymmetry in electron scattering.
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