Radical subgroups of lattice ordered groups
Random Cayley graphs are expanders: a simple proof of the Alon-Roichman theorem.
Random walks on co-compact fuchsian groups
It is proved that the Green’s function of a symmetric finite range random walk on a co-compact Fuchsian group decays exponentially in distance at the radius of convergence . It is also shown that Ancona’s inequalities extend to , and therefore that the Martin boundary for -potentials coincides with the natural geometric boundary , and that the Martin kernel is uniformly Hölder continuous. Finally, this implies a local limit theorem for the transition probabilities: in the aperiodic case, .
Random walks on finite rank solvable groups
We establish the lower bound , for the large times asymptotic behaviours of the probabilities of return to the origin at even times , for random walks associated with finite symmetric generating sets of solvable groups of finite Prüfer rank. (A group has finite Prüfer rank if there is an integer , such that any of its finitely generated subgroup admits a generating set of cardinality less or equal to .)
Rank analogues of Hall's and Baer's theorems.
Rank gradient, cost of groups and the rank versus Heegaard genus problem
We study the growth of the rank of subgroups of finite index in residually finite groups, by relating it to the notion of cost. As a by-product, we show that the ‘rank vs. Heegaard genus’ conjecture on hyperbolic 3-manifolds is incompatible with the ‘fixed price problem’ in topological dynamics.
Rational L-groups of Bieberbach groups.
Real Elements in Small Cancellation Groups.
Real Strict Localizations.
Realisierung von Gruppen PSL2 (IFp) als Galoisgruppen über Q.
Realization of finitely generated profinite groups by maximal abelian extensions of fields.
Realizing countable groups as automorphism groups of Riemann surfaces.
Receding polar regions of a spherical building and the center conjecture
We introduce the notion of a polar region of a spherical building and use some simple observations about polar regions to give elementary proofs of various fundamental properties of root groups. We combine some of these observations with results of Timmesfeld, Balser and Lytchak to give a new proof of the center conjecture for convex chamber subcomplexes of thick spherical buildings.
Recherche des graphes des matrices de Coxeter hyperboliques d’ordre
Rechtsteilweise geordnete Gruppen
Recognizability in the lattice of convex -subgroups of a lattice-ordered group
Rectificatif à l'article «Présentation de certains couples fischériens de type classique»
Recursively Presented Two Generated Infinite p-Groups.
Reduced Forms for Quadratic Words and Spines of 2-manifolds.
Regular geodesic languages and the falsification by fellow traveler property.