This volume assembles research papers in geometric and combinatorial group theory. This wide area may be defined as the study of those groups that are defined by their action on a combinatorial or geometric object, in the spirit of Klein's programme.

The contributions range over a wide spectrum: limit groups, groups associated with equations, with cellular automata, their structure as metric objects, their decomposition, etc. Their common denominator is the language of group theory, used to express and solve problems ranging from geometry to logic.

Contains contributions from experts in geometric and combinatorial group theory, most of which were present at the Geneva and Barcelona conferences in 2005 Above the diversity of the articles included in this volume reigns a strong unity of themes and purposes: understanding geometrical and logical objects through their symmetries Witnesses to the power of group theory as a language for expressing, communicating and solving problems throughout mathematics Contains particularly two articles by A. Juhász on the solution of the membership problem for Magnus subgroups and on the solution of the conjugacy problem and malnormality of subgroups Includes supplementary material: sn.pub/extras

Zusammenfassung

This volume has its origins in the Barcelona Conference in Group Theory (July 2005) and the conference "Asymptotic and Probabilistic Methods in Geometric Group Theory" held in Geneva (June 2005). Twelve peer-reviewed research articles written by experts in the field present the most recent results in abstract and geometric group theory. In particular there are two articles by A. Juhász.

Inhalt
Totally Disconnected, Locally Compact Groups as Geometric Objects.- Computational Explorations in Thompson's Group F.- On the Surjunctivity of Artinian Linear Cellular Automata over Residually Finite Groups.- Some Residually Finite Groups Satisfying Laws.- Classifying Spaces for Wallpaper Groups.- A General Construction of JSJ Decompositions.- Décompositions de Groupes par Produit Direct et Groupes de Coxeter.- Limit Groups of Equationally Noetherian Groups.- Solution of the Conjugacy Problem and Malnormality of Subgroups in Certain Relative Small Cancellation Group Presentations.- Solution of the Membership Problem for Magnus Subgroups in Certain One-Relator Free Products.- Conjugacy and Centralizers for Iwip Automorphisms of Free Groups.- Algebraic Extensions in Free Groups.