  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 $h_1^q$ are nowadays well established. Several possible channels to
access these functions were originally proposed. One candidate is the
measurement of the polarisation of $\Lambda$ 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
$\Lambda$ and $\bar{\Lambda}$ 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 $h_1^u$
and $h_1^d$.
