under the orders of; by order of
Fixed formal expression used when an action is taken on someone's command or authority. Often appears in official or historical contexts.
He started a new project under the orders of the company president.
The soldier acted by order of his superior officer.
Standard kanji spelling for this fixed expression.
Explicit kanji spelling using 依る; less common and may appear formal or literary.
Combination of 命 (order, command) + により (formal expression meaning 'by' or 'according to'). The phrase is a fixed formal construction.