Algebraic extensions in free groups

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical fieldt heoretic notions, and we discuss in detail the notion of algebraic closure. We apply that theory to the study and the computation of certain algebraic properties of subgroups (e.g. being malnormal, pure, inert or compressed, being closed in certain profinite topologies) and the corresponding closure operators. We also analyze the closure of a subgroup under the addition of solutions of certain sets of equations.

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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Evaluation of an antireflux procedure for colonic interposition in pediatric esophageal replacements.

Background: In 1989, we introduced a 1-stage procedure with orthotopic colonic transplants for esophageal stenosis. A pitfall of this procedure is frequent reflux and/or stasis in the transplants from the cologastric anastomosis. Since 1993, we have used a new antireflux wrap (ARW) using an anterior wrap technique similar to the Dor procedure but fixed to the right crus of the diaphragm.Purpose: The purpose of the study was to evaluate ARWs.Method: From 1993 to 2008, the records of 67 patients with an ARW were compared with 27 without ARW (either operated on before 1993 or ARW was not appropriate) after colonic transplant for caustic esophageal stenosis. Both groups otherwise underwent the same surgical procedure. Postoperative esophagograms done on postoperative day 10 were reviewed for the presence of gastrocolonic reflux and stasis in the transplant.Results: The reflux rate on the initial esophagogram was reduced from 48.1% to 7.5% using ARW. The incidence of reflux on later esophagograms was 40.0% with no ARW and 21.4% with ARW. The 25% long-term rate of stasis in the colonic transplant was not increased with ARW.Conclusions: A loose ARW in patients with colonic esophageal replacements reduces gastrocolic reflux without increasing the rate of stasis. In the long term, children adapt better to stasis than to reflux and are thus protected from occult inflammation.

Extracorporeal membrane oxygenation support after heart explantation: a proposal on how to deal with hyperacute rejection of heart transplant

Purpose: In extreme situations, such as hyperacute rejection of heart transplant or major bleeding per-operating complications, an urgent heart explantation might be the only means of survival. The aim of this experimental study was to improve the surgical technique and the hemodynamics of an Extracorporeal Membrane Oxygenation (ECMO) support through a peripheral vascular access in an acardia model. Methods: An ECMO support was established in 7 bovine experiments (59±6.1 kg) by the transjugular insertion to the caval axis of a self-expanded cannula, with return through a carotid artery. After baseline measurements of pump flow and arterial and central venous pressure, ventricular fibrillation was induced (B), the great arteries were clamped, the heart was excised and right and left atria remnants, containing the pulmonary veins, were sutured together leaving an atrial septal defect (ASD) over the cannula in the caval axis. Measurements were taken with the pulmonary artery (PA) clamped (C) and anastomosed with the caval axis (D). Regular arterial and central venous blood gases tests were performed. The ANOVA test for repeated measures was used to test the null hypothesis and a Bonferroni t method for assessing the significance in the between groups pairwise comparison of mean pump flow. Results: Initial pump flow (A) was 4.3±0.6 L/min dropping to 2.8±0.7 L/min (P B-A= 0.003) 10 minutes after induction of ventricular fibrillation (B). After cardiectomy, with the pulmonary artery clamped (C) it augmented not significantly to 3.5±0.8 L/min (P C-B= 0.33, P C-A= 0.029). Finally, PA anastomosis to the caval axis was followed by an almost to baseline pump flow augmentation (4.1±0.7 L/min, P D-B= 0.009, P D-C= 0.006, P D-A= 0.597), permitting a full ECMO support in acardia by a peripheral vascular access. Conclusions: ECMO support in acardia is feasible, providing new opportunities in situations where heart must urgently be explanted, as in hyperacute rejection of heart transplant. Adequate drainage of pulmonary circulation is pivotal in order to avoid pulmonary congestion and loss of volume from the normal right to left shunt of bronchial vessels. Furthermore, the PA anastomosis to the caval axis not only improves pump flow but it also permits an ECMO support by a peripheral vascular access and the closure of the chest.

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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A classification, up to hyperbolicity, of groups given by 2 generators and one relator of length 8

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