What is a good thesis on the exercising of power in Lord of the Flies?
One thesis is the transfer of symbolic power from the conch to Piggy's glasses.
Initially, the boys are united in their efforts to survive. Ralph is the leader. Although he takes that role seriously, he is not greedy for power. In fact, he does his best to delegate authority and certain jobs, thereby displacing the responsibility. At the early stages, the only symbol of power is the conch, which allows anyone to speak but in an orderly way. This is a logical organization and Ralph is likely the most just and fair leader on the island.
When Jack starts to pull away from the group, others follow. The shift of power is complete when Jack and his group steal Piggy's glasses. Piggy's glasses become the symbol of power because the glasses are the most technologically advanced tool the boys have on the island. Chapter 10 is called "The Shell and the Glasses." Jack and his crew attack Ralph's camp. Ralph and Piggy assume they came to steal the conch. When Jack ignores the conch and steals the glasses, the symbol of power has shifted from the conch to the glasses:
The chief led then, trotting steadily, exulting in his achievement. He was a chief now in truth; and he made stabbing motions with his spear. From his left hand dangled Piggy’s broken glasses.
When Piggy and Ralph fail to retrieve the glasses, the end result is that Piggy is killed senselessly (because at this point, Piggy is completely vulnerable, not to mention he never was a threat to anyone); and when Piggy dies, the conch is destroyed as well. The symbolic shift of power from the conch to the glasses is complete.