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

TL;DR

This paper verifies the inductive Feit and Galois-McKay conditions for certain small-rank simple groups of Lie Type, including PSL2(q) and Suzuki groups, advancing the understanding of their representation theory.

Contribution

It completes the proof of the inductive Feit and Galois-McKay conditions for PSL2(q) and shows Suzuki groups satisfy the inductive Feit condition, extending previous results.

Findings

Confirmed inductive Feit condition for PSL2(q)

Proved Suzuki groups satisfy the inductive Feit condition

Advances in understanding simple groups of Lie Type

Abstract

We complete the proof of the inductive Feit condition and the inductive Galois-McKay condition for the simple groups $\operatorname{PSL}_2(q)$. We also prove that the Suzuki groups $^{2}B_2(2^{2n+1})$ satisfy the inductive Feit condition.