$S{p}_6(2^a)$ is "Good" for the McKay, Alperin Weight, and Related Local-Global Conjectures

Abstract

The so-called "local-global" conjectures in the representation theory of finite groups relate the representation theory of $G$ to that of certain proper subgroups, such as the normalizers of particular $p$-groups. Recent results by several authors reduce some of these conjectures to showing that a certain collection of stronger conditions holds for all finite simple groups. Here, we show that $G=S{p}_6(2^a)$ is "good" for these reductions for the McKay conjecture, the Alperin weight conjecture, and their blockwise versions.

References in corpus (2)

• Quasi-isolated blocks and Brauer's height zero conjecture
• Cross-Characteristic Representations of $S{p}_6(2^a)$ and Their Restrictions to Maximal Subgroups

Cited by in corpus (1)

• The inductive Alperin-McKay and blockwise Alperin weight conditions for blocks with cyclic defect groups