Jack shows lots of violence in this book. Perhaps the first time he is really violent is when they kill the pig. He gets his hunters to kill the sow, and then they torture the poor thing.
Next comes the chanting around their fire: "Kill the beast! Cut his throat! Spill his blood!" Simon is coming out of the woods and they attack him when Jack yells that Simon is really the beast. They kill Simon. That is the first murder on this island.
Then in chapter 10, when Ralph tries to talk to Jack, he sees that Willard has been receiving a beating from Jack just because Jack wants to beat him. Now his violence is just for show. This leads up to the end when Jack and Roger try to burn out Ralph and finally kill him.
Compared in the end of "Lord of the Flies" to an ape and a savage, Jack represents the complete unleashing of man's base, primal nature. As such his reactions to situations become increasingly more violent as the narrative continues. These actions are motivated by his jealousy of Ralph and Piggy, whose behavior is adult/civilized as well as by his fear, of which he is ashamed.
Capitalizing upon the fear of the others, however, Jack is able to manipulate the boys such as SamnEric whom he intimidates into following him. In fact, it is this fear that leads to the violence and savage behavior that unleashes the "beast" in their souls.
In Chapter 7 Jack's increasing cruelty emerges after the boys pretend to kill the pig and hurt Robert instead and Jack suggests using a littl'un next time when they practice. Later, when Jack hides behind the paint, his violent nature emerges: He boldly steals the fire and dances naked in front of Ralph. Having usurped authority, Jack becomes more savage, beating one of the boys in Chapter 10. When Piggy accuses Jack of stealing his glasses, Jack rushes at him with his spear. Then, when Ralph, enraged, calls Jack and his boys "painted fools," Jack fights Ralph. Piggy tries to restore order, but is struck by a rock and falls to his death; Jack threatens Ralph with the same end, hurling his spear at Ralph.
In the final chapter, his savage nature has full reign as Jack orders a fire to flush out Ralph, not reasoning that this fire will destroy the entire island. As Shakespeare wrote, "Violent delights oft have violent ends."