Related papers: Commensurability in Artin groups of spherical type

Let K be the quotient field of a complete local domain of dimension 2 with a separably closed residue field. Let G be a finite group of order not divisible by char(K). Then G is admissible over K if and only if its Sylow subgroups are…

An $n$-ary operation $Q:S^n -> S$ is called an $n$-ary quasigroup of order $|S|$ if in the equation $x_{0}=Q(x_1,...,x_n)$ knowledge of any $n$ elements of $x_0$, ..., $x_n$ uniquely specifies the remaining one. $Q$ is permutably reducible…

Let $F$ be a $p$-adic field, and let $G$ be either the split special orthogonal group $\mathrm{SO}_{2n+1}(F)$ or the symplectic group $\mathrm{Sp}_{2n}(F)$, with $n \geq 0$. We prove that a smooth irreducible representation of good parity…

In this paper we consider the class of 2-dimensional Artin groups with connected, large type, triangle-free defining graphs (type CLTTF). We classify these groups up to isomorphism, and describe a generating set for the automorphism group…

(1) We prove that, provided n>=4, a permutably reducible n-ary quasigroup is uniquely specified by its values on the n-ples containing zero. (2) We observe that for each n,k>=2 and r<=[k/2] there exists a reducible n-ary quasigroup of order…

We prove that for any natural n>1, the abstract commensurator group of the Baumslag - Solitar group BS(1,n) is isomorphic to the group of 2 by 2 upper triangular matrices A over rational numbers with A_{11}=1. We also prove that for any…

We study a moduli space AS_g for Artin-Schreier curves of genus g over an algebraically closed field k of characteristic p. We study the stratification of AS_g by p-rank into strata AS_{g,s} of Artin-Schreier curves of genus g with p-rank…

An irreducible character of a finite group $G$ is called quasi $p$-Steinberg character for a prime $p$ if it takes a nonzero value on every $p$-regular element of $G$. In this article, we classify the quasi $p$-Steinberg characters of…

Arthur has conjectured that the unitarity of a number of representations can be shown by finding appropriate automorphic realizations. This has been verified for classical groups by Moeglin and for the exceptional Chevalley group G_2 by…

Two finitely generated groups have the same set of finite quotients if and only if their profinite completions are isomorphic. Consider the map which sends (the isomorphism class of) an S-arithmetic group to (the isomorphism class of) its…

Let $G$ be a finite group and $K$ a finite field of characteristic $2$. Denote by $t$ the $2$-rank of the commutator factor group $G/G'$ and by $s$ the number of self-dual simple $KG$-modules. Then the Witt group of equivariant quadratic…

Let R be a ring and G a group. An R-module A is said to be artinian-by-(finite rank) if TorR(A) is artinian and A/TorR(A) has finite R-rank. The authors study ZG-modules A such that A/CA(H) is artinian-by-(finite rank) (as a Z-module) for…

It is well known that if two finite groups have the same symmetric tensor categories of representations over C, then they are isomorphic. We study the following question: when do two finite groups G1,G2 have the same tensor categories of…

Let $\Gamma\subset\mathbb{Q}^*$ be a finitely generated subgroup and let $p$ be a prime such that the reduction group $\Gamma_p$ is a well defined subgroup of the multiplicative group $\mathbb{F}_p^*$. We prove an asymptotic formula for the…

The result of this paper is the determination of the cohomology of Artin groups of type A_n, B_n and \tilde{A}_{n} with non-trivial local coefficients. The main result is an explicit computation of the cohomology of the Artin group of type…

Let $\mathrm{Mod}(S)$ be the mapping class group of a compact connected orientable surface $S$, possibly with punctures and boundary components, with negative Euler characteristic. We prove that for any infinite virtually abelian subgroup…

Commensurable groups are bi-interpretable, under suitable definability conditions.

In this short note we answer to a question of group theory from arXiv:0910.5080. In that paper the author describes the set of realizable Steinitz classes for so-called $A'$-groups of odd order, obtained iterating some direct and semidirect…

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.

We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building…