Distortion of wreath products in some finitely presented groups

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Infinite index subgroups and finiteness properties of intersections of geometrically finite groups

We explore which types of finiteness properties are possible for intersections of geometrically finite groups of isometries in negatively curved symmetric rank one spaces. Our main tool is a twist construction which takes as input a geometrically finite group containing a normal subgroup of infinite index with given finiteness properties and infinite Abelian quotient, and produces a pair of geometrically finite groups whose intersection is isomorphic to the normal subgroup.

Minimal truncations of supersingular p-divisible groups

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The mean dehn functions of Abelian groups

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Traverso's isogeny conjecture for p-divisible groups

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Minimal lenght elements of Thompson's groups F(p)

We describe a method for determining the minimal length of elements in the generalized Thompson's groups F(p). We compute the length of an element by constructing a tree pair diagram for the element, classifying the nodes of the tree and summing associated weights from the pairs of node classifications. We use this method to effectively find minimal length representatives of an element.

Contraction groups in complete Kac-Moody groups

Let G be an abstract Kac-Moody group over a finite field and G the closure of the image of G in the automorphism group of its positive building. We show that if the Dynkin diagram associated to G is irreducible and neither of spherical nor of affine type, then the contraction groups of elements in G which are not topologically periodic are not closed. (In those groups there always exist elements which are not topologically periodic.)

Parabolic and quasiparabolic subgroups of free partially commutative groups

Let Γ be a finite graph and G be the corresponding free partially commutative group. In this paper we study subgroups generated by vertices of the graph Γ, which we call canonical parabolic subgroups. A natural extension of the definition leads to canonical quasiparabolic subgroups. It is shown that the centralisers of subsets of G are the conjugates of canonical quasiparabolic centralisers satisfying certain graph theoretic conditions.

Discriminating groups: a comprehensive overview

Discriminating groups were introduced by G.Baumslag, A.Myasnikov and V.Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. However they have taken on a life of their own and have been an object of a considerable amount of study. In this paper we survey the large array results concerning the class of discriminating groups that have been developed over the past decade.

The equation xpyq=zr and groups that act freely on Λ-trees

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Occurrence and bioaccumulation study of PCDD and PCDF from mineral feed additives

Occurrence of polychlorinated dibenzo-p-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs) was evaluated in sepiolite as a widely employed binder and anti-caking agent for animal feed. Also, naturally contaminated kaolinitic clay was used for comparative purposes. Since sepiolite shows remarkable adsorption properties, particular interest was paid to the extraction steps as they become critical for the final determination of these pollutants in such matrixes. Furthermore, classical Soxhlet extraction using different extracting strategies as well as acid treatment were carried out with simultaneous liquid-liquid extraction. Results obtained depended on the extraction procedure applied. Acid treatment or Soxhlet extraction using a mixture of toluene:ethanol as solvent allowed to reach the minimum requirements of recovery rates. However, Soxhlet extraction using a mixture cyclohexane:toluene as extracting solvent did not allow to comply with minimum specifications for recovery. Significant differences were obtained in TEQ units when acid treatment was applied in comparison to Soxhlet extraction. This fact can be explained because the use of drastic acid conditions allows removing strongly adsorbed analytes which can be uniquely extracted after a total destruction of the crystalline structure of sepiolite. On the contrary, Soxhlet extraction was not able to destroy the structure of sepiolite and as a consequence the PCDDs/Fs were strongly adsorbed in the internal structure of the mineral. From biological point of view the availability of these toxicants constitutes a critical aspect playing an important role in the final decision choosing particular analytical procedures. Then, acid conditions in the digestive tract should be taken into account. In this scenario, a bioaccumulation study was conducted to evaluate the transference of PCDDs/PCDFs from the sepiolite into the animal tissues when fed with feed containing sepiolite. To this end, chickens were used as a model to examine the bioavailability of PCDDs/PCDFs. Four groups of chickens were exposed through their diet to a control feed, feed with 3% w/w sepiolite as additive, feed contaminated with PCDDs/PCDFs at concentration around 2.8 pg WHO-TEQ/g and feed with 2% of a contaminated kaolinitic clay (460 pg TEQ/g mineral). Livers of the four studied groups were analyzed throughout the exposure period. Results of this trial showed that the performance of broilers was not affected by the presence of dioxins at levels tested, and chickens did not show any abnormal behaviour. Dioxins intentionally added to the diet were absorbed and accumulated in the liver in a significant manner, whereas the PCDDs/Fs from sepiolite were not available for chickens since livers from broilers fed 3% sepiolite presented similar WHO-TEQ values than those from broilers fed control diet.

Orbit decidability and the conjugacy problem for some extensions of groups

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Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Metric properties of the braided Thompson's groups

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On the intersection of free subgroups in free products of groups

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