The inductive blockwise Alperin weight condition for $G_2(q)$ and $^3D_4(q)$

TL;DR

This paper verifies the inductive blockwise Alperin weight condition for the finite simple groups G_2(q) and ^3D_4(q), advancing the proof of the blockwise Alperin weight conjecture.

Contribution

It establishes the inductive blockwise Alperin weight condition for G_2(q) and ^3D_4(q), covering all primes dividing their order.

Findings

Condition verified for G_2(q) and ^3D_4(q)

Supports the blockwise Alperin weight conjecture

Progress in classification of simple groups

Abstract

The inductive blockwise Alperin weight condition is a system of conditions whose verification for all non-abelian finite simple groups would imply the blockwise Alperin weight conjecture. We establish this condition for the groups $G_2(q)$, $q \geq 5$, and $^3D_4(q)$ for all primes dividing their order.