A military police force or the buildings and institutions where military police operate; armed police or constabulary troops.
From French 'gendarmerie,' itself from 'gendarme' (armed police), which comes from French 'gens d'armes' meaning 'men of arms.' This entered English in the 18th century describing French and European military police forces.
Gendarmes in France were 'gens d'armes'—'men of arms'—and gendarmery is where they operate, usually in rural areas; it's why you see similar police forces across Europe with this French-origin name.
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