In this note we extend to metrizable profinite groups the classical theorems of Titchmarsh on the Fourier transform of H\"older-Lipschitz functions. This generalizes the results of Younis on compact zero-dimensional abelian groups to the noncommutative case, and proves a relation between the H\"older-Lipschitz-continuity of functions and their Sobo...
La théorie de Bass-Serre a été développée en 1970 par Jean-Pierre Serre, dans [Ser77]. Elle a pour motivation principale d'étudier la structure des sous-groupes discrets et sans torsion de SL2(Qp), plus précisément le théorème d'Ihara suivant lequel ces sous-groupes sont libres. S'inspirant de la topologie notamment de la théorie des revêtements, i...
Published in Lobachevskii Journal of Mathematics
We prove some conditions on a given abstract group G, such that the group Autc(G^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat G$$\end{document}) of the continuo...
There has been much recent interest into those properties of a 3-manifold determined by the profinite completion of its fundamental group. In this paper we give readily computable criteria specifying precisely when two orientable graph manifold groups have isomorphic profinite completions. Our results also distinguish graph manifolds among the clas...
Dans cette thèse, nous nous intéressons aux sous-groupes profinis et pro-p d'un groupe algébrique linéaire connexe défini sur un corps local. Dans le premier chapitre, on résume brièvement la théorie de Bruhat-Tits et on introduit les notations nécessaires à ce travail. Dans le second chapitre, on trouve des conditions équivalentes à l'existence de...
Published in São Paulo Journal of Mathematical Sciences
A brief introduction to Brauer Theory, emphasizing functorial aspects that allow for a natural extension to profinite groups. Based on joint work with Peter Symonds.
Published in Archiv der Mathematik
For several natural filtrations of a free group S, we express the n-th term of the filtration as the intersection of all kernels of homomorphisms from S to certain groups of upper-triangular unipotent matrices. This generalizes a classical result of Grün for the lower central filtration. In particular, we do this for the n-th term in the lower p-ce...
Published in Archiv der Mathematik
We consider profinite groups in which all commutators are contained in a union of finitely many procyclic subgroups. It is shown that if G is a profinite group in which all commutators are covered by m procyclic subgroups, then G possesses a finite characteristic subgroup M contained in G′ such that the order of M is m-bounded and G′/M is procyclic...
Published in Journal of Algebra
Published in Journal of Algebra
