If Γ1, . . . ,Γn are limit groups and S ⊂ Γ1 × · · · × Γn is of type FPn(Q) then S contains a subgroup of finite index that is itself a direct product of at most n limit groups. This answers a question of Sela.

Complete presentations provide a natural solution to the word problem in monoids and groups. Here we give a simple way to construct complete presentations for the direct product of groups, when such presentations are available for the factors. Actually, the construction we are referring to is just the classical construction for direct products of groups, which has been known for a long time, bu...

The Product Conjecture for the homological Bieri-Neumann-StrebelRenz invariants is proved over a field. Under certain hypotheses the Product Conjecture is shown to also hold over Z, even though D. Schütz has recently shown that the Conjecture is false in general over Z. Our version over Z is applied in a joint paper with D. Kochloukova [5] to show that for all n Thompson’s group F contains subg...

We apply the theory of height zeta functions to study the asymptotic distribution of rational points of bounded height on projective equivariant compactifications of semi-direct products. Introduction Let X be a smooth projective variety over a number field F and L a very ample line bundle on X. An adelic metrization L = (L, ‖ · ‖) on L induces a height function HL : X(F )→ R>0, let N(X◦,L,B) :...