  The global polarization of {\Lambda} hyperons along the total orbital angular
momentum of a relativistic heavy-ion collision is presented based on the high
statistics data samples collected in Au+Au collisions at \sqrt{s_{NN}} = 2.4
GeV and Ag+Ag at 2.55 GeV with the High-Acceptance Di-Electron Spectrometer
(HADES) at GSI, Darmstadt. This is the first measurement below the strangeness
production threshold in nucleon-nucleon collisions. Results are reported as a
function of the collision centrality as well as a function of the hyperon
transverse momentum (p_T) and rapidity (y_{CM}) for the range of centrality
0--40%. We observe a strong centrality dependence of the polarization with an
increasing signal towards peripheral collisions. For mid-central (20--40%)
collisions the polarization magnitudes are <P_{\Lambda}>(%) = 6.8 \pm 1.3
(stat.) \pm 2.1 (syst.) for Au+Au and <P_{\Lambda}>(%) = 6.2 \pm 0.4 (stat.)
\pm 0.6 (syst.) for Ag+Ag, which are the largest values observed so far. This
observation thus provides a continuation of the increasing trend previously
observed by STAR and contrasts expectations from recent theoretical
calculations predicting a maximum in the region of collision energies about 3
GeV. The observed polarization is of a similar magnitude as predicted by 3D
fluid dynamics and the UrQMD plus thermal vorticity model and significantly
above results from the AMPT model.
