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[References.: 53 tit.]

Based on the observation of sizeable target-transverse-spin asymmetries in single-hadron and hadron-pair production in Semi-Inclusive measurements of Deep Inelastic Scattering (SIDIS), the chiral-odd transversity quark distribution functions ℎ1 are nowadays well established. Several possible channels to access these functions were originally proposed. One candidate is the measurement of the polarisation of Λ hyperons produced in SIDIS off transversely polarised nucleons, where the transverse polarisation of the struck quark might be transferred to the final-state hyperon. In this article, we present the COMPASS results on the transversity-induced polarisation of Λ and Λ¯ hyperons produced in SIDIS off transversely polarised protons. Within the experimental uncertainties, no significant deviation from zero was observed. The results are discussed in the context of different models taking into account previous experimental results on ℎ1 and ℎ1.