What is the German equivalent to the idiom under someone's thumb.
Even if not exactly, is there any phrase having similar meaning?
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You would say (jemanden) unter der Fuchtel haben as an equivalent figurative expression.
For the record:
Die Fuchtel ist ein Degen mit breiter Klinge. Schläge mit der flachen Seite der Fuchtel waren eine übliche Strafe im preußischen Heer. [The Fuchtel is a rapier/sword with a wide blade. Blows with the flat side of the Fuchtel was a customary punishment in the Prussian army.]
I'd say "unter der Fuchtel stehen" or the opposite "den Daumen drauf haben" when there is no personal relationship between the participants. "Unter dem Pantoffel stehen", due to the mention of the very private, informal footwear ;), to me implies an intimate relationship.