We study the transverse polarization of hyperons produced
in semi-inclusive deep inelastic scattering, $ep \to e\Lambda^{\uparrow}X$,
in the collinear twist-3 factorization. This process receives three types of
twist-3 contributions: (i) twist-3 distribution in the initial proton combined
with the transversity fragmentation function (FF) for the hyperon,
(ii) Twist-3 quark FFs for the hyperon, and (iii) Twist-3 gluon FFs for the hyperon.
In this talk, we present the twist-3 cross section for (iii) in the leading order (LO)
with respect to the QCD coupling constant, which completes the LO cross section
for this process. Since gluons are ample in the nucleons,
this contribution
representing multi-gluon correlations in the fragmentation process is
potentially as important as other two contributions.
This study is relevant for the future
Electron-Ion Collider experiment.