Inductive Feit and Galois-McKay conditions for some small-rank simple groups of Lie Type

We complete the proof of the inductive Feit condition and the inductive Galois-McKay condition for the simple groups ${\mathrm{PSL}}_2(q)$. We also prove that the Suzuki groups ${}^2{B}_2(2^{2n+1})$ satisfy the inductive Feit condition.