I would say that the first of Jack's important actions is his attempt to be the chief of the boys. Ralph and Jack are put up for election, and Jack loses. He's not happy about it, but Jack is placated with being put in charge of the group's hunting efforts.
A second important event is Jack failing to kill the first pig that he comes across. He raises his knife to kill it, but he can't go through with it. The result is that he vows to not show any mercy next time.
Jack is so obsessed with hunting and killing a pig that he and his boys forget to tend the signal fire. The result is that a ship passed the island and never noticed the boys.
Jack slowly takes control of the group and steals Piggy's glasses. Now Jack has all of the control.
Jack attempts to hunt and kill Ralph. To do this, Jack starts a big fire to smoke Ralph out. A passing Navy ship sees the fire and rescues the remaining boys.