Inductive blockwise Alperin weight condition for type B and odd primes

TL;DR

This paper proves the inductive blockwise Alperin weight condition for simple groups of type B at odd primes, advancing the verification process for the Alperin weight conjecture in finite group theory.

Contribution

It establishes the inductive blockwise Alperin weight condition for type B simple groups at odd primes using a recent criterion by Brough and Sp"ath.

Findings

Verified the inductive blockwise Alperin weight condition for type B groups.

Extended the validity of the Alperin weight conjecture to new classes of groups.

Abstract

By the reduction theorems of Navarro--Tiep and Sp\"ath, a way to prove the Alperin weight conjecture and its blockwise version is to verify the co-called inductive Alperin weight condition and inductive blockwise Alperin weight condition for all finie simple groups respectively. In this paper, we establish the inductive blockwise Alperin weight condition for simple groups of type $\mathsf B$ and odd primes, using a criterion given by Brough and Sp\"ath recently.