Hyperbolic groups have flat-rank at most 1

Reduced fusion systems over 2 - groups of sectional rank at most 4

We classify all reduced, indecomposable fusion systems over finite 2-groups of sectional rank at most 4. The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional 2-rank at most 4. But our method of proof is very different from theirs, and is based on an analysis of the essential subgroups which can occur in the fusion systems. 2010 Mathematics Subjec...

Verbal subgroups of hyperbolic groups have infinite width

Some Groups Whose Reduced C {algebras Have Stable Rank One

It is proved that, for the following classes of groups, ?, the reduced group C-algebra C (?) has stable rank 1: (i) hyperbolic groups which are either torsion{free and non{elementary or which are cocom-pact lattices in a real, noncompact, simple, connected Lie group of real rank 1 having trivial center; (ii) amalgamated free products of groups, ? = G 1 H G 2 , where H is nite and there is g 0 2...

The Groups of Order at Most 2000

We announce the construction up to isomorphism of the 49 910 529 484 groups of order at most 2000.

Hyperbolic groups with 1-dimensional boundary

If a torsion-free hyperbolic group G has 1-dimensional boundary ∂∞G, then ∂∞G is a Menger curve or a Sierpinski carpet provided G does not split over a cyclic group. When ∂∞G is a Sierpinski carpet we show that G is a quasiconvex subgroup of a 3-dimensional hyperbolic Poincaré duality group. We also construct a “topologically rigid” hyperbolic group G: any homeomorphism of ∂∞G is induced by an ...