Radix redux: Normal subgroups of symplectic groups.
Ramanujan-Identitäten zur Reziproken der Jacobischen Funktion .. .
R-and T-Groupoids: A Generalization of 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 .)
Random walks on groups and monoids with a Markovian harmonic measure.
Range of density measures
We investigate some properties of density measures – finitely additive measures on the set of natural numbers extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence as well as cluster points of some other similar sequences. We obtain range of possible values of density measures for any subset of . Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao [Bhaskara Rao, K. P. S., Bhaskara Rao,...
Range sets and partition sets in connection with congruences and algebraic invariants.
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.
Rank three residually connected geometries for , revisited.
Ranks of binary relations.
Rational actions associated to the adjoint representation
Rational and Generic Cohomology
Rational fixed points for linear group actions
We prove a version of the Hilbert Irreducibility Theorem for linear algebraic groups. Given a connected linear algebraic group , an affine variety and a finite map , all defined over a finitely generated field of characteristic zero, Theorem 1.6 provides the natural necessary and sufficient condition under which the set contains a Zariski dense sub-semigroup ; namely, there must exist an unramified covering and a map such that . In the case , is the additive group, we reobtain the...
Rational Functions Invariant under a Finite Abelian Group.
Rational Homology of Bianchi Groups.
Rational L-groups of Bieberbach groups.
Rational Lie Algebras and p-Isomorphisms of Nilpotent Groups and Homotopy Types.