One of the first times where Jack and Ralph truly disagree on an important issue is in chapter 2. One of the young boys describes "the beast" for the first time. Ralph denies the existence of "the beast" while Jack validates its existence by promising to hunt and kill it.
In chapter 3 Ralph and Jack argue again, but this time more seriously. They argue because Jack is more interested in hunting than any other responsibility, however, Ralph feels that hunting should be second to things like shelter and keeping the fire going. Their unresolved differences lay between them like a wedge. “They looked at each other, baffled, in love and hate. All the warm salt water of the bathing pool and the shouting and splashing and laughing were only just sufficient to bring them together again.”
These are examples of the developing conflict. The conflict escalates in each chapter. In the fourth chapter there is a conflict regarding Jack's negligence of the fire. The conflicts escalate and escalate until finally the boys form two different groups and split up.