Related papers: Finiteness properties of arithmetic groups over fu…

By an $\ell$-group $G$ we mean a lattice-ordered abelian group. This paper is concerned with the category $\FP$ of finitely presented {\it unital} $\ell$-groups, those $\ell$-groups having a distinguished order-unit $u$. Using the duality…

Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…

In this report we summarize this work, all finite simple groups $G$ can determined uniformly using their orders $|G|$ and the set $\pi_e(G)$ of their element orders.

We survey some results on the structure of the groups which are definable in theories of fields involved in the applications of model theory to Diophantine geometry. We focus more particularly on separably closed fields of finite degree of…

In this paper we describe all group gradings by a finite abelian group G of any Lie algebra L of the type "A" over algebraically closed field F of characteristic zero.

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F, or more generally, of a bounded PAC field F. This paper answers some of the questions of [1], and in particular that any finite group…

We obtain several finiteness results for the unramified cohomology of function fields of algebraic varieties defined over fields of type (F'_m), a class that includes algebraically closed fields, finite fields, local fields, and some higher…

We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.

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…

We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we show that any sequence of finite-dimensional representations…

Various problems on integers lead to the class of congruence preserving functions on rings, i.e. functions verifying $a-b$ divides $f(a)-f(b)$ for all $a,b$. We characterized these classes of functions in terms of sums of rational…

This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…

We outline a general procedure that builds classifying spaces for generalized Thompson groups $\Gamma$. The construction depends on a small number of choices: (1) an inverse semigroup $S$ of partial transformations that ``locally determine"…

We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi-Brauer surfaces over fields of characteristic zero.

We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.

Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.

For an odd prime $p$, let $\phi$ denote the quadratic character of the multiplicative group ${\mathbb F}_p^\times$, where ${\mathbb F}_p$ is the finite field of $p$ elements. In this paper, we will obtain evaluations of the hypergeometric…

We study topological full groups attached to groupoid models for left regular representations of Garside categories. Groups arising in this way include Thompson's group $V$ and many of its variations such as R\"over-Nekrashevych groups. Our…

We define Langlands parameters for connected reductive groups over finite fields and formulate the Langlands correspondence for finite fields using these parameters.

We study rational functions over finite fields under PGL-equivalence. We say that $f, g \in \Bbb F_q(X)$ are \emph{equivalent} if there exist $\psi, \phi \in \Bbb F_q(X)$ of degree one such that $g = \psi \circ f \circ \phi$. Most…