Related papers: Simple endotrivial modules for quasi-simple groups

We organize fundamental properties of quasi-Hamiltonian spaces on which a finite group acts, and we apply them to the theory of moduli spaces of flat connections on an oriented compact surface with boundary.

The aim of this work is to give a description of the locally trivial monodromy group of irreducible symplectic varieties arising from moduli spaces of semistable sheaves on Abelian surfaces with non-primitive Mukai vector. The outcome is…

We consider metric ultraproducts of finite groups with respect to some classes of length functions. All sofic groups embed into these ultraproducts. We study embeddings of normed groups. We also show that in some natural situations such an…

The first-order model theory of modules has been studied for decades. More recently, the model theoretic study of nonelementary classes of modules--especially Abstract Elementary Classes of modules--has produced interesting results. This…

We define the notion of an additive model category, and we prove that any additive, stable, combinatorial model category has a natural enrichment over symmetric spectra based on simplicial abelian groups. As a consequence, every object in…

In the arithmetic of function fields Drinfeld modules play the role that elliptic curves take on in the arithmetic of number fields. As higher dimensional generalizations of Drinfeld modules, and as the appropriate analogues of abelian…

We describe "quasi canonical modules" for modular invariant rings $R$ of finite group actions on factorial Gorenstein domains. From this we derive a general "quasi Gorenstein criterion" in terms of certain 1-cocycles. This generalizes a…

We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a…

We show that a differential algebraic group can be filtered by a finite subnormal series of differential algebraic groups such that successive quotients are almost simple, that is have no normal subgroups of the same type. We give a…

This paper is a contribution to the construction of non-semisimple modular categories. We establish when M\"uger centralizers inside non-semisimple modular categories are also modular. As a consequence, we obtain conditions under which…

In this paper, we investigate the notions of almost Noetherian rings and modules. In details, we give the Cohen type theorem, Eakin-Nagata type theorem, Kaplansky type Theorem and Hilbert basis theorem and some other rings constructions for…

We determine subnormalisers of semisimple elements of prime power order in finite quasi-simple groups of Lie type. For this, we determine the maximal overgroups of normalisers of Sylow tori. This is motivated by the recent character…

A B-group is a group such that all its minimal generating sets (with respect to inclusion) have the same size. We prove that the class of finite B-groups is closed under taking quotients and that every finite B-group is solvable. Via a…

Suppose that $G$ is a finite group such that $\operatorname{SL}(n,q)\subseteq G \subseteq \operatorname{GL}(n,q)$, and that $Z$ is a central subgroup of $G$. Let $T(G/Z)$ be the abelian group of equivalence classes of endotrivial…

Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to…

Let $p$ be a prime. In this paper, we compute complexities of some simple modules of symmetric groups labelled by two-part partitions. Most of the simple modules considered here are contained in the $p$-blocks with non-abelian defect…

Every cotilting module over a ring R induces a t-structure with a Grothendieck heart in the derived category D(Mod R). We determine the simple objects in this heart and their injective envelopes, combining torsion-theoretic aspects with…

Simple-minded systems in stable module categories are defined by orthogonality and generating properties so that the images of the simple modules under a stable equivalence form such a system. Simple-minded systems are shown to be invariant…

We discuss the notion of essential dimension of a finite group and explain its relation with birational algebraic geometry. We show how this leads to a (partial) classification of simple finite groups of essential dimension less than or…

This paper investigates the asymptotic behaviour of the minimal number of generators of finite index subgroups in residually finite groups. We analyze three natural classes of groups: amenable groups, groups possessing an infinite soluble…