Authority is mentioned in the Quran in these verses:
[2:30] Recall that your Lord said to the angels, “I am placing a representative (a temporary god) on Earth.” They said, “Will You place therein one who will spread evil therein and shed blood, while we sing Your praises, glorify You, and uphold Your absolute authority?” He said, “I know what you do not know.”
[4:54] Are they envious of the people because God has showered them with His blessings? We have given Abraham’s family the scripture, and wisdom; we granted them a great authority.
[7:54] Your Lord is the one God, who created the heavens and the earth in six days, then assumed all authority. The night overtakes the day, as it pursues it persistently, and the sun, the moon, and the stars are committed to serve by His command. Absolutely, He controls all creation and all commands. Most Exalted is God, Lord of the universe.
[10:3] Your only Lord is God; the One who created the heavens and the earth in six days, then assumed all authority. He controls all matters. There is no intercessor, except in accordance with His will. Such is God your Lord. You shall worship Him. Would you not take heed?
[11:96] We sent Moses with our signs and a profound authority.
[13:2] God is the One who raised the heavens without pillars that you can see, then assumed all authority. He committed the sun and the moon, each running (in its orbit) for a predetermined period. He controls all things, and explains the revelations, that you may attain certainty about meeting your Lord.
[14:10] Their messengers said, “Do you have doubts about God; the Initiator of the heavens and the earth? He invites you only to forgive your sins, and to give you another chance to redeem yourselves.” They said, “You are no more than humans like us, who want to repel us from the way our parents used to worship. Show us some profound authority.”
[17:33] You shall not kill any person – for God has made life sacred – except in the course of justice. If one is killed unjustly, then we give his heir authority to enforce justice. Thus, he shall not exceed the limits in avenging the murder; he will be helped.
[18:84] We granted him authority on earth, and provided him with all kinds of means.
[20:5] The Most Gracious; He has assumed all authority.
[21:22] If there were in them (the heavens and the earth) other gods beside God, there would have been chaos. Glory be to God; the Lord with absolute authority. He is high above their claims.
[23:116] Most exalted is God, the true Sovereign. There is no other god beside Him; the Most Honorable Lord, possessor of all authority.
[25:59] He is the One who created the heavens and the earth, and everything between them, in six days, then assumed all authority. The Most Gracious; ask about Him those who are well founded in knowledge.
[28:35] He said, “We will strengthen you with your brother, and we will provide you both with manifest authority. Thus, they will not be able to touch either one of you. With our miracles, the two of you, together with those who follow you, will be the victors.”
[32:4] God is the One who created the heavens and the earth, and everything between them in six days, then assumed all authority. You have none beside Him as Lord, nor do you have an intercessor. Would you not take heed?
[40:23] We sent Moses with our signs and a profound authority.
[53:6] Possessor of all authority. From His highest height.
[53:26] Not even the angels in heaven possess authority to intercede. The only ones permitted by God are those who act in accordance with His will and His approval.
[57:4] He is the One who created the heavens and the earth in six days, then assumed all authority. He knows everything that enters into the earth, and everything that comes out of it, and everything that comes down from the sky, and everything that climbs into it. He is with you wherever you may be. God is Seer of everything you do.
To learn more, read the Quran in English.
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