The classification of the finite simple groups is considered as one of the greatest
achievements in mathematics of the twentieth century. The result provides the most basic …

The Alperin weight conjecture is central to the modern representation theory of finite groups,
and it is still open, despite many different approaches from different points of view. This …

We classify all 2‐blocks with abelian defect groups of rank 4 up to Morita equivalence. The
classification holds for blocks over a suitable discrete valuation ring as well as for those over …

The Alperin–McKay conjecture is a longstanding open conjecture in the representation
theory of finite groups. Späth showed that the Alperin–McKay conjecture holds if the so …

Recently, G. Navarro introduced a new conjecture that unifies the Alperin Weight Conjecture
and the Glauberman correspondence into a single statement. In this paper, we reduce this …

We give a reduction to quasisimple groups for Donovan's conjecture for blocks with abelian
defect groups defined with respect to a suitable discrete valuation ring O O. Consequences …

Let $\ell $ be a prime number. We show that the Morita Frobenius number of an $\ell $-block
of a quasi-simple finite group is at most $4 $ and that the strong Frobenius number is at most …

Donovan’s conjecture and blocks with abelian defect groups Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 147, Number 3, March 2019, Pages 963–970 …

We give a lower bound on the Loewy length of a p-block of a finite group in terms of its
defect. We then discuss blocks with small Loewy length. Since blocks with Loewy length at …

We classify the Morita equivalence classes of blocks with elementary abelian defect groups
of order $16 $ with respect to a complete discrete valuation ring with algebraically closed …