Jack's rise to power accompanies his growing lust for violence.  He solidifies his position among the choir boys, "the hunters" after they make their first kill. 

"Jack spoke loudly.

'This head is for the beast. It's a gift.'

The silence accepted the gift and awed them." (137)

After Jack plunges the head onto the stick "sharpened at both ends," his willing act of violence impresses the boys.  They view him reverently, because he has fearlessly taken the violence to the next level, committing acts they only dreamed about before. 

His dominance solidifies after the brutal death of Piggy.  After the death of the sow, Golding emphasizes a moment of silence--that the boys are in awe of the acts committed, a reverent moment of silence, almost--as if in appreciation.  The same is true when Piggy dies.  Golding writes: "This time the silence was complete" (181).  This time Jack breaks the silence powerfully, revealing his dominance as chief:

"Suddenly Jack bounded out from the tribe and began screaming wildly. 

'See?  See? That's what you'll get! I meant that! There isn't a tribe for you anymore! The conch is gone--

He ran forward, stooping.

"I'm chief!" (181)

Even though Jack is not the one who murders Piggy; his blatant acceptance of his murder both terrifies and impresses the other boys.  His savagery complete, Jack's willingness to accept and use violence upon others intimidates the other boys, who are unwilling or too frightened to go against him.