This article combines the features of a survey and a research paper. It presents a review of
some results obtained during the last decade in problems related to the dynamics of branch …

We study C⁎-irreducibility of inclusions of reduced twisted group C⁎-algebras and of
reduced group C⁎-algebras. We characterize C⁎-irreducibility in the case of an inclusion …

Finding the number of maximal subgroups of infinite index of a finitely generated group is a
natural problem that has been solved for several classes of “geometric” groups (linear …

Branch groups, a class of groups defined through their action on a rooted tree, play an
important role in group theory, since they often possess rare properties that cannot be found …

An action of a group G is highly transitive if G acts transitively on k-tuples of distinct points for
all k⩾ 1. Many examples of groups with a rich geometric or dynamical action admit highly …

Marden's Tameness Conjecture predicts that every hyperbolic 3-manifold with finitely
generated fundamental group is homeomorphic to the interior of a compact 3-manifold. It …

A group Γ is sharply 2-transitive if it admits a faithful permutation representation that is
transitive and free on pairs of distinct points. Conjecturally, for all such groups there exists a …

The purpose of this article is to produce effective versions of some rigidity results in algebra
and geometry. On the geometric side, we focus on the spectrum of primitive geodesic …

Highly transitive actions of Out.Fn/ Page 1 Groups Geom. Dyn. 7 (2013), 357–376 DOI
10.4171/GGD/185 Groups, Geometry, and Dynamics © European Mathematical Society Highly …

The transitivity degree of a group GG is the supremum of all integers kk such that GG admits
a faithful kk‐transitive action. Few obstructions are known to impose an upper bound on the …