Conjectures of Alperin and Broue for 2-blocks with elementary abelian defect groups of order 8

TL;DR

This paper proves Alperin's weight conjecture and Broue's abelian defect group conjecture for 2-blocks with elementary abelian defect groups of order 8, utilizing the classification of finite simple groups.

Contribution

It provides the first proof of these conjectures for this specific class of blocks, expanding the understanding of block theory in finite groups.

Findings

Confirmed Alperin's weight conjecture for the specified blocks.

Validated Broue's abelian defect group conjecture in this context.

Established new links between simple group classification and block theory.

Abstract

Using the classification of finite simple groups we prove Alperin's weight conjecture and the character theoretic version of Broue's abelian defect group conjecture for 2-blocks of finite groups with an elementary abelian defect group of order 8.