Related papers: Blocks whose defect groups are Suzuki $2$-groups

We prove that blocks of the general linear supergroup are Morita equivalent to a limiting version of Khovanov's diagram algebra. We deduce that blocks of the general linear supergroup are Koszul.

We characterize finite groups having a cyclic Sylow p-subgroup in terms of the action of a specific Galois automorphism on the principal p-block for p=2,3. We show that the analog statement for blocks with arbitrary defect group would…

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…

We prove that if $b$ is a block of a finite group with normal abelian defect group and inertial quotient a direct product of elementary abelian groups, then $\operatorname{Picent}(b)$ is trivial. We also provide examples of blocks $b$ of…

In this paper, we investigate the block that has an abelian defect group of rank $2$ and its Brauer correspondent has only one simple module. We will get an isotypy between the block and its Brauer correspondent. It will generalize the…

We prove the Alperin-McKay Conjecture for all $p$-blocks of finite groups with metacyclic, minimal non-abelian defect groups. These are precisely the metacyclic groups whose derived subgroup have order $p$. In the special case $p=3$, we…

We consider the localisation of the 2-category of diffeological groupoids at weak equivalences from the perspective of anafunctors, and with this language, prove that the localisation of the 2-category of Lie groupoids is an essentially…

We determine the combinatorial depth of certain subgroups of simple Suzuki groups Sz(q), among others the depth of their maximal subgroups. We apply these results to determine the ordinary depth of these subgroups.

We prove a conjecture of Broue about the Jordan decomposition of blocks of finite reductive groups. We show that a block of a finite connected reductive group, in non-describing characteristic, is Morita-equivalent to a quasi-isolated block…

The Eaton--Moret\'o conjecture extends the recently-proven Brauer height zero conjecture to blocks with non-abelian defect group, positing equality between the minimal positive heights of a block of a finite group and its defect group. Here…

This paper is an attempt to compute the decomposition numbers of the blocks of the symmetric group which have "small defect"; that is, blocks of weight smaller than the characteristic. We present various methods for computing such…

This article proves a version of the Feit-Thompson theorem for simple groups of finite Morley rank: a connected groups of finite Morley rank with a finite Sylow 2-subgroup has a trivial Sylow 2-subgroups.

We consider a natural generalisation of symmetric Nakayama algebras, namely, symmetric special biserial algebras with at most one non-uniserial indecomposable projective module. We describe the basic algebras explicitly by quiver and…

A derived version of Maschke's theorem for finite groups is proved: the derived categories, bounded or unbounded, of all blocks of the group algebra of a finite group are simple, in the sense that they admit no nontrivial recollements. This…

For a finite group $G$ and a positive integer $n$, let $G(n)$ be the set of all elements in $G$ such that $x^{n}=1$. The groups $G$ and $H$ are said to be of the same (order) type if $G(n)=H(n)$, for all $n$. The main aim of this paper is…

It is shown that Section 8 of Plesken's 1983 lecture notes describes blocks of cyclic defect group up to Morita equivalence. In particular such a block is determined by its planar embedded Brauer tree. Applying the radical idealizer…

We compute explicitly up to Morita-equivalence the skew group algebra of a finite group acting on the path algebra of a quiver and the skew group algebra of a finite group acting on a preprojective algebra. These results generalize previous…

Over an arbitrary field, we prove that the relative 2-Deligne tensor product of two separable module 2-categories over a compact semisimple tensor 2-category exists. This allows us to consider the Morita 4-category of compact semisimple…

We characterize the inverse semigroups that are Morita equivalent to graph inverse semigroups. We also consider a generalization to inverse semigroups associated with left cancellative categories.

In by now classical work, K. Erdmann classified blocks of finite groups with dihedral defect groups (and more generally algebras of dihedral type) up to Morita equivalence. In the explicit description by quivers and relations of such…