Why did Solomon have Adonijah, Joab and Shimei put to death?

The chapter gives Solomon's own words for each and adds no verdict of its own. When Adonijah asks for Abishag the Shunammite as his wife (2:17) and Bathsheba brings the request (2:21), Solomon answers his mother, "Ask for him the kingdom also, for he is my elder brother; even for him, and for Abiathar the priest, and for Joab the son of Zeruiah" (2:22), and swears, "surely Adonijah shall be put to death today" (2:24). Adonijah had said to Bathsheba, "You know that the kingdom was mine" (2:15), and in chapter 1 Solomon had spared him on a condition: "if wickedness is found in him, he shall die" (1:52). The chapter doesn't explain further why the request meant what Solomon said it meant. Of Joab the narrator says, "Joab had followed Adonijah, although he didn’t follow Absalom" (2:28), and Solomon names the blood Joab had shed: "that you may take away the blood, which Joab shed without cause, from me and from my father’s house" (2:31), the blood of Abner and Amasa (2:32). To Shimei, Solomon names the oath he broke (2:42-43) and "all the wickedness that you did to David my father" (2:44). Abiathar, who had also followed Adonijah (1:7), is told, "you are worthy of death" (2:26), and spared for what he had done with David (2:26). The chapter closes, "The kingdom was established in the hand of Solomon" (2:46).