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Group Extensions with Infinite Conjugacy Classes

Jean-Philippe Préaux — 2013

Confluentes Mathematici

We characterize the group property of being with infinite conjugacy classes (or , infinite and of which all conjugacy classes except { 1 } are infinite) for groups which are extensions of groups. We prove a general result for extensions of groups, then deduce characterizations in semi-direct products, wreath products, finite extensions, among others examples we also deduce a characterization for amalgamated products and HNN extensions. The icc property is correlated to the Theory of von Neumann algebras...

Groupes fondamentaux des variétés de dimension 3 et algèbres d’opérateurs

Pierre de la HarpeJean-Philippe Préaux — 2007

Annales de la faculté des sciences de Toulouse Mathématiques

Nous proposons une caractérisation géométrique des variétés de dimension  3 ayant des groupes fondamentaux dont toutes les classes de conjugaison autres que  { 1 } sont infinies, c’est-à-dire dont les algèbres de von Neumann sont des facteurs de type  I I 1   : ce sont essentiellement les 3 -variétés à groupes fondamentaux infinis qui n’admettent pas de fibration de Seifert. Autrement dit et plus précisément, soient  M une 3 -variété connexe compacte et Γ son groupe fondamental, qu’on suppose être infini et avec...

Testing Cayley graph densities

Goulnara N. ArzhantsevaVictor S. GubaMartin LustigJean-Philippe Préaux — 2008

Annales mathématiques Blaise Pascal

We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an m -generated group is amenable if and only if the density of the corresponding Cayley graph equals to 2 m . We test amenable and non-amenable...

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