This is the 5523rd most frequent Spanish word.
permitiéndoles
"Allowing them" or "permitting them."
In this sentence, 'permitiéndoles' indicates enabling or allowing a group of individuals to perform an action (entering the building).
Les abrieron las puertas, permitiéndoles entrar al edificio.
They opened the doors for them, allowing them to enter the building.
'Permitiéndoles' here denotes facilitating or allowing a group to complete a process (applying for visas).
Los ayudaron con la documentación, permitiéndoles solicitar sus visas.
They helped them with the documentation, allowing them to apply for their visas.
The use of 'permitiéndoles' shows that an action (providing access to classes) grants the possibility or permission to achieve a goal (improving skills).