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.

Weighted Hardy spaces for the unit disc: approximation properties

In this paper we study basic properties of the weighted Hardy space for the unit disc with the weight function satisfying Muckenhoupt's (Aq) condition, and study related approximation problems (expansion, moment and interpolation) with respect to two incomplete systems of holomorphic functions in this space.

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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Política de la competència de la Unió Europea en el sector audiovisual. El cas dels operadors públics estatals de televisió a Espanya i el Regne Unit: RTVE i BBC

Estudi elaborat a partir d’una estada al Center for Socio-Legal Studies de la Universitat d’Oxford, Gran Bretanya, entre setembre del 2006 i gener del 2007. L'objectiu d'aquesta recerca ha estat determinar i avaluar com la política de la competència de la Unió Europea ha contribuït a la configuració del sector públic televisiu espanyol i britànic. El marc teòric està basat en el concepte d’ “europeització”, desenvolupat per Harcourt (2002) en el sector de mitjans, i que implica una progressiva referencialitat de les polítiques estatals amb les europees mitjançant dos mecanismes: la redistribució de recursos i els efectes en la socialització de la política europea. Per tal de verificar aquest impacte en el sector televisiu, la recerca ha desenvolupat una aproximació en dues etapes. En primer lloc, a banda de fer un inicial repàs bibliogràfic s'han estudiat les accions de la Comissió Europea en aquest terreny, sobre tot la Comunicació sobre aplicació de la reglamentació d'ajudes públiques al sector de la radiodifusió de 2001. En una segona etapa, s'han desenvolupat un seguit d'entrevistes personals a directius i polítics del sector a Brussel•les, Londres i Madrid. Els resultats de la recerca mostren que el procés d’Europeïtzació es un fenomen creixent en el sector audiovisual públic a Espanya i el Regne Unit, però que encara les peculiaritats estatals juguen un factor preponderant en regular aquesta influència de la UE. L'anàlisi de les entrevistes qualitatives mostren també que hi ha una relació inversament proporcional entre la tradició democràtica i el grau d’influència i de referència que suposa la UE en el sector audiovisual. Mentre que el Regne Unit, l'acció de la política de la competència de la UE es percep com a element suplementari, a Espanya la seva referencialitat ha estat clau, tot i que no decisiva, per la reforma dels mitjans públics estatals.  

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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Social polarization: introducing distances between and within groups

The measurement of social polarization has received little attention from the literature. The only social polarization index that has been used to measure religious or ethnic polarization (the RQ index) has several shortcomings that are critically discussed in the paper. In particular, that index is not taking into account the existing distance between and within different groups. A couple of axiomatically characterized social polarization indices that overcome these limitations are presented. In the empirical section we show that the rankings of countries according to the levels of polarization change to a great extent when we replace the RQ index by the indices presented in this paper.