hubieron permitido
-they/you had allowed
Preterite perfectellos/ellas/ustedesconjugation ofpermitir.

permitir

Pero la mayoría de estos trabajadores no tuvieron nada claro qué hacer después de que hubieron permitido que la burocracia sindical se insinuase al movimiento que había tratado de impedir.
But most of these workers were unclear enough as to what to do next that they allowed the union bureaucracy to insinuate itself into the movement it had tried to prevent.
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