Jordan tori for a torsion free abelian group

Divisibility Properties of Group Rings over Torsion-free Abelian Groups

Let G be a torsion-free abelian group of type (0, 0, 0, . . . ) and R an integrally closed integral domain with quotient field K. We show that every divisorial ideal (respectively, t-ideal) J of the group ring R[X;G] is of the form J = hIR[X;G] for some h ∈ K[X;G] and a divisorial ideal (respectively, t-ideal) I of R. Consequently, there are natural monoid isomorphisms Cl(R) ∼= Cl(R[X;G]) and C...

A Superposition Calculus for Divisible Torsion-Free Abelian Groups

Uniquely Transitive Torsion-free Abelian Groups

We will answer a question raised by Emmanuel Dror Farjoun concerning the existence of torsion-free abelian groups G such that for any ordered pair of pure elements there is a unique automorphism mapping the first element onto the second one. We will show the existence of such a group of cardinality λ for any successor cardinal λ = μ+ with μ = μ0.

Jump degrees of torsion-free abelian groups

We show, for each computable ordinal α and degree a > 0(α), the existence of a torsion-free abelian group with proper αth jump degree a.

A theorem on torsion free Kleinian group

Let H be the hyperbolic 3-space and IsomH be the group of isometries of H. Let G be a discrete subgroup of IsomH. The action of G on H extends to a continuous action on the compactification of H by the sphere at infinity S ∞. The limit set Λ(G) is the set of all accumulation points of the orbit of a point in H. The limit set does not depend on the choice of the point in H and the limit set is a...