On ordered polycyclic groups

On Ordered Polycyclic Groups

It has been asserted that any (full) order on a torsion-free, finitely generated, nilpotent group is defined by some F-basis of G and that the group of o-automorphisms of such a group is itself a group of the same kind: Examples provided herein demonstrate that both of these assertions are false; however, it is proved that the group of o-automorphisms of an ordered, polycyclic group is nilpoten...

Aperiodic Subshifts on Polycyclic Groups

We prove that every polycyclic group of nonlinear growth admits a strongly aperiodic SFT and has an undecidable domino problem. This answers a question of [5] and generalizes the result of [2]. Subshifts of finite type (SFT for short) in a group G are colorings of the elements of G subject to local constraints. They have been studied extensively for the free abelian group Z [14] and on the free...

Generation of polycyclic groups

Polycyclic groups are one of the best understood class of groups. For example most of the decision problems are decidable in this class, see [7]. It seems surprising therefore that it is still an open problem whether there exists an algorithm which finds d(G) for any polycyclic group G (given by say a set of generators and relations). This is unknown even in the case when G is virtually abelian...

Compressions on Partially Ordered Abelian Groups

If A is a C*-algebra and p ∈ A is a self-adjoint idempotent, the mapping a 7→ pap is called a compression on A. We introduce effect-ordered rings as generalizations of unital C*-algebras and characterize compressions on these rings. The resulting characterization leads to a generalization of the notion of compression on partially ordered abelian groups with order units.

Shanks Workshop on Ordered Groups in Logic