Related papers: Double centralizers in Artin-Tits groups

We show that stable equivalences between Artin algebras without nodes preserve homological data that provide upper bounds for finitistic dimension, and that stable equivalences between Artin algebras with positive $\nu$-dominant dimensions…

We prove a second main theorem for elliptic projective planes.

We present in this work a new and simple proof of the false centre theorem.

In this article, we prove an analog of the classical collar lemma in the setting of Hitchin representations.

We prove the Farrell-Jones fibered isomorphism conjecture for several classes of Artin groups of finite and affine types. As a consequence, we compute explicitly the surgery obstruction groups of the finite type pure Artin groups.

According to the Tits conjecture proved by Crisp and Paris, [CP], the subgroups of the braid group generated by proper powers of the Artin elements are presented by the commutators of generators which are powers of commuting elements. Hence…

In this note we formulate a conjecture about two group ring identities and prove that it would imply the Alon-Jaeger-Tarsi conjecture.

In this second paper we solve the twisted conjugacy problem for even dihedral Artin groups, that is, groups with presentation $G(m) = \langle a,b \mid {}_{m}(a,b) = {}_{m}(b,a) \rangle$, where $m \geq 2$ is even, and $_{m}(a,b)$ is the word…

We prove a duality theorem for quantum groupoid (weak Hopf algebra) actions that extends the well-known result for usual Hopf algebras.

Provides a counterexample to a long standing conjecture of A. Adem regarding the behaviour of the integral cohomology of a p-group.

This paper is a sequel of [A.M. Cohen, L. Paris, {\it On a theorem of Artin}, J. Group Theory {\bf 6} (2003), 421--441]. Let $A$ be an Artin group, let $W$ be its associated Coxeter group, and let $CA$ be its associated coloured Artin…

We generalize Artin's three main algebraicity theorems to the setting of supergeometry: Artin approximation, algebraization of formal moduli, and algebraization of stacks.

We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.

In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However,…

We give an algebraic proof for a theorem of Mislin in the case of cohomology of saturated fusion systems defined on p-groups when p is odd. Some applications of this theorem to block algebras of finite groups are also given.

Let G be a finite p-group and let Aut_l(G) be the group of absolute central automorphisms of G. We give necessary and sufficient conditions on G such that Aut_l(G) = Inn(G).

We prove that in a connected group of finite Morley rank the centralizers of decent tori are connected. We then apply this result to the analysis of minimal connected simple groups of finite Morley rank. Our applications include general…

In this paper, we consider covers of finite groups by centralizers of elements. We show that the set of centralizers that are maximal under the partial ordering form a cover of the group. We also show that the set of centralizers that are…

Let G be an isotropic reductive algebraic group over a commutative ring R. Assume that, for any maximal ideal M of R, the rank of the relative root system of G_{R_M} is greater or equal than 2. We show that under this assumption the…

We study centralisers of finite order automorphisms of generalisations of Thompson's group F and conjugacy classes of finite subgroups in finite extensions of these groups. In particular, we show that centralisers of finite automorphisms in…