Related papers: Weak almost monomial groups and Artin's conjecture

The concept of a C-approximable group, for a class of finite groups C, is a common generalization of the concepts of a sofic, weakly sofic, and linear sofic group. Glebsky raised the question whether all groups are approximable by finite…

This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has received relatively little attention, but…

Let $G$ be a finite almost simple group with socle $G_0$. In this paper we prove that whenever $G/G_0$ is abelian, then there exists an abelian subgroup $A$ of $G$ such that $G=AG_0$. We propose a few applications of this structural…

Over a scheme of finite type over a field of characteristic zero, we prove that Nori an Voevodsky categories of relative Artin motives, that is the full subcategories generated by the motives of \'etale morphisms in relative Nori and…

Let $L/K$ be a Galois extension of number fields. We prove two lower bounds on the maximum of the degrees of the irreducible complex representations of ${\rm Gal}(L/K)$, the sharper of which is conditional on the Artin Conjecture and the…

It was conjectured at the end of the book "Representation theory of Artin algebras" by M. Auslander, I. Reiten and S. Smalo that an Artin algebra with the property that its finitely generated indecomposable modules are up to isomorphism…

We prove several results on the model theory of Artin groups, focusing on Artin groups which are ``far from right-angled Artin groups''. The first result is that if $\mathcal{C}$ is a class of Artin groups whose irreducible components are…

Sp\"ath showed that the Alperin-McKay conjecture in the representation theory of finite groups holds if the so-called inductive Alperin-McKay condition holds for all finite simple groups. In a previous article, we showed that the…

The Farrell-Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example for discrete subgroups of Lie groups, virtually poly-infinite cyclic groups, Artin…

Let $R$ be a semilocal principal ideal domain. Two algebraic objects over $R$ in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all…

We prove that the Flat Cover Conjecture holds for the category of (right) acts over any right-reversible monoid $S$, provided that the flat $S$-acts are closed under stable Rees extensions. The argument shows that the class…

Let $\Lambda$ be an artin algebra. We are going to consider full subcategories of $\mod\Lambda$ closed under finite direct sums and under submodules with infinitely many isomorphism classes of indecomposable modules. The main result asserts…

The purpose of this paper is to constructively develop a Galois theory on irreducible shifts of finite type (SFTs) and to analyze the automorphism groups of SFTs using this framework. Let $X$ and $Y$ be irreducible SFTs. We demonstrate that…

A split extension of monoids with kernel k: N -> G, cokernel e: G -> H and splitting s: H -> G is weakly Schreier if each element g in G can be written g = k(n)se(g) for some n in N. The characterization of weakly Schreier extensions allows…

This paper focuses on a refinement of the inverse Galois problem. We explore what finite groups appear as the Galois group of an extension of the rational numbers in which only a predetermined set of primes may ramify. After presenting new…

Let $G$ and $G'$ be two right-angled Artin groups (RAAG). We show they are quasi-isometric iff they are isomorphic, under the assumption that $Out(G)$ and $Out(G')$ are finite. If only $Out(G)$ is finite, then $G'$ is quasi-isometric $G$…

Let $G$ be a right-angled Artin group with $|\mathrm{Out}(G)|<+\infty$. We prove that if a countable group $H$ with bounded torsion is measure equivalent to $G$, with an $L^1$-integrable measure equivalence cocycle towards $G$, then $H$ is…

Let $k$ be an imaginary quadratic number field, and $F/k$ a finite abelian extension of Galois group $G$. We show that a Gross conjecture concerning the leading terms of Artin $L$-series holds for $F/k$ and all rational primes which are…

A result by Bridson, Howie, Miller, and Short states that if $S$ is a finitely presented subgroup of the direct product of free groups, then $S$ is virtually a nilpotent extension of a direct product of free groups. Moreover, if $S$ is a…

We show that the class of groups satisfying the K- and L-theoretic Farrell-Jones conjecture is closed under taking graph products of groups.