“Who gave him the 'authority' to do this?” “He didn't do it 'on his own authority' [=he didn't do it on his own]; he was acting 'under the authority of' the company president.” [=the company president gave him the power to do it]
No one 'in authority' objected to the plan. = No one 'in a position of authority' objected to the plan. [=no one with official power to make important decisions objected to the plan]
This office has 'authority' over personnel matters. [=this office has the power to make decisions about personnel matters]
(..) Stop here! Who commands here? I am the emissary... ...to the ruler of all the world... ...the god of gods, king of kings... ...and by that authority... ...I demand that someone show me your commander. Listen. Do you think the paltry dozen you slew scares us? These hills swarm with our scouts. (..)2006 300