Cantor systems, piecewise translations and simple amenable groups
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Non-positively curved spaces admitting a cocompact isometric action of an amenable group are investigated. A classification is established under the assumption that there is no global fixed point at infinity under the full isometry group. The visual bounda ...
We propose elementary and explicit presentations of groups that have no amenable quotients and yet are SQ-universal. Examples include groups with a finite K (pi,1), no Kazhdan subgroups and no Haagerup quotients. ...
The aim of this paper is to construct an equivalent of the Dade group of a p-group for an arbitrary finite group G, whose elements are equivalences classes of endo-p-permutation modules. To achieve this goal we use the theory of relative projectivity with ...
We describe various classes of infinitely presented groups that are condensation points in the space of marked groups. A well-known class of such groups consists of finitely generated groups admitting an infinite minimal presentation. We introduce here a l ...
Grigorchuk and Medynets recently announced that the topological full group of a minimal Cantor Z-action is amenable. They asked whether the statement holds for all minimal Cantor actions of general amenable groups as well. We answer in the negative by prod ...
Let G be any group containing an infinite elementary amenable subgroup and let 2 < p < infinity. We construct an exhaustion of l(p) G by closed invariant subspaces which all intersect trivially a fixed non-trivial closed invariant subspace. This is an obst ...
We give a complete characterization of the locally compact groups that are nonelementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover gi ...
Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C*-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UC ...
Thévenaz [6] made an interesting observation that the number of conjugacy classes of cyclic subgroups in a finite group G is equal to the rank of the matrix of the numbers of double cosets in G. We give another proof of this fact and present a fusion syste ...
Consider a proper cocompact CAT(0) space X. We give a complete algebraic characterisation of amenable groups of isometries of X. For amenable discrete subgroups, an even narrower description is derived, implying Q-linearity in the torsion-free case. We est ...
