Where does “fugák” come from?

fugák (Hungarian) comes from Hungarian fúga, from German füge, from German fügen, from Old High German fuogen, from Proto-West Germanic fōgijan, from Proto-Germanic fōgijaną, from Proto-Germanic fōgō, from Proto-Indo-European peh₂ḱ- — to join, to attach; agreement, settlement.

Ancestry of “fugák”, step by step

StepLanguageWordMeaning
1Hungarianfúgafugue
2Germanfügeinflection of fügen: ## first-person singular...
3Germanfügento join; to add; to ordain
4Old High Germanfuogento add; to connect
5Proto-West Germanicfōgijanto fit together, to join
6Proto-Germanicfōgijanąto fit or join together
7Proto-Germanicfōgōjoint, slot
8Proto-Indo-Europeanpeh₂ḱ-to join, to attach; agreement, settlement
Every word from Proto-Indo-European peh₂ḱ-Every word from Proto-Germanic fōgōEvery word from Proto-Germanic fōgijaną