Nomen

der Mitgliedsantrag

membership application

Ich muss den Mitgliedsantrag noch ausfüllen.

I still have to fill out the membership application.

Sein Mitgliedsantrag wurde angenommen.

His membership application was accepted.

to submit/fill out ((a membership application)). You have to submit a membership application.

der Aufnahmeantrag (application for admission), der Beitrittsantrag (application to join)

A compound of 'Mitglied' (member) and 'Antrag' (application, request). Literally a 'member application'.

It's an 'Antrag' (application) to become a 'Mitglied' (member). Simple as that.

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