Donovan's conjecture and blocks with abelian defect groups

TL;DR

This paper reduces Donovan's conjecture for abelian defect groups to a case involving quasisimple groups and confirms its validity specifically for abelian 2-groups.

Contribution

It establishes a reduction of Donovan's conjecture to quasisimple groups and proves the conjecture for abelian 2-groups.

Findings

Reduction of Donovan's conjecture to quasisimple groups

Proof of Donovan's conjecture for abelian 2-groups

Advancement in understanding blocks with abelian defect groups

Abstract

We give a reduction of Donovan's conjecture for abelian groups to a similar statement for quasisimple groups. Consequently we show that Donovan's conjecture holds for abelian $2$-groups.