Jack shows his power over Piggy from the very first time they meet when he tells Piggy to shut up. Throughout the book Jack continually speaks dismissively to Piggy, telling him that he isn't wanted on the expedition to the mountain, calling him a fat slug during a meeting and continually belittling the fat boy. Piggy is fully aware that Jack hates him and Jack makes this abundantly clear for everyone to see. Refusing to give Piggy any meat and punching him are two further examples of Jack demonstrating his power and physical prowess over the fat and ineffectual Piggy.
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At first Jack tries to get the boys to revote and make him chief but when the boys vote again for Ralph he gets angry and storms of to create his own more "fun" camp. He invites anyone who wants to join and hunt with him. Everyone ends up leaving Ralphs tribe and they become savages.
Ralph and Jack never liked each other. Once they met and Jack wanted to take the power from Ralph there was instant friction between the two. It's was obviously Ralph's job to be chief and Jack just expected to get it instead of Ralph.
Ralph takes Simon and Jack along with him on the expedition.
Because 1: Piggy and Ralph got the conch they used as a talking power in the assemblies; 2:Ralph is still the leader after all; 3: Piggy owns the specs, he has the power to take what he owns back in a civilized group(but apparently it is not)
They took Piggy´s glasses, but didn´t take the conch. The conch is only a symbol of authority and has power only when the society agrees that it does. For Jack, the shell is, now, only a shell. The glasses, however, give him real power because he is the only one with the ability to start a fire. "He was a chief now, in truth." (Pg. 168)
Jack attacked Piggy rather than Ralph because he knew Piggy wouldn't fight back. If he had attacked Ralph there was a good chance that Ralph would have beaten him and Jack couldn't take the risk of losing face in front of his own hunters.