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The premises of a property consist of the land and buildings on it, usually of a business or organization. If there are no dogs allowed on the premises of a school, you'll have to leave your furry friend at home. (Vocabulary.com)
Ground and grounds should not be confused. Grounds are the area around a building or an area of land which has common ownership in which case either in or on are possible: The pond is located in the grounds of the stately mansion. On the grounds behind the castle they have hunting. (StackExchange)
The crime was committed on American soil. (Longman Dictionary of Contemporary English)
