“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]
(..) A girlfriend? Yes, sir. She lives next door. This is for your own good, boy. You have no respect for other people's things and for authority... Yes, sir. I'm sorry. Can't just go around doing whatever you feel like. You can't. There are rules in life. (..)1999 American Beauty