Before revision:  More precisely, we need to find a set of k centers C so as to minimize the maximum over all groups j of u \text{ in group j} d(u,C)^p. The socially fair clustering problem was independently proposed by Abbasi, Bhaskara, and Venkatasubramanian [2021] and Ghadiri, Samadi, and Vempala [2021].
After revision:  More precisely, we need to find a set of k centers C so as to minimize the maximum over all groups j of u \text{ in group j} d(u,C)^p. The socially fair clustering problem was independently proposed by Ghadiri, Samadi, and Vempala [2021] and Ghadiri, Samadi, and Vempala [2021].