Let us just quickly remind ourselves of the key point to this brilliant story. The reason that the citizens of Omelas are able to enjoy such incredible and unbelievable wealth, prosperity and happiness is precisely because all unhappiness is bestowed on the poor child that is described to us at the heart of the story. It is the ultimate example of utilitarianism, which believes that the happiness of the many is always to be chosen over the happiness of the few. In some strange way, the suffering of that poor child ensures the happiness of the citizens of Omelas. Therefore, the child is the only example of social inequality you are going to find in this short story. And what an example of social inequality this child presents us with:
The child used to scream for help at night, and cry a good deal, but now it only makes a kind of whining, "eh-haa, eh-haa," and it speaks less and less often. It is so thin there are no calves to its legs; its belly protrudes; it lives on a half-bowl of corn meal and grease a day. It is naked. Its buttocks and thighs are a mass of festered sores, as it sits in its own excrement continually.
This story then posits an ideal and perfect society that is only able to be ideal and perfect because of the systematic abuse and mistreatment of one child. This story asks if the price of this perfect society is too high, or is it acceptable given the state of happiness of the citizens of Omelas. The only example of social inequality in Omelas is this child, and so a thesis statement you could use might be as follows:
In "The Ones Who Walk Away from Omelas," the author creates a fantasy world where the citizens of Omelas are able to enjoy happiness and prosperity that is only possible because of the unhappiness and abuse of a child.
This thesis statement will allow you to talk about social inequality and how it is reflected in the character of the poor child who suffers so much so that others may experience happiness.