Endogenous population subgroups: the best population partition and optimal number of groups

The aim of this paper is to suggest a method to find endogenously the points that group the individuals of a given distribution in k clusters, where k is endogenously determined. These points are the cut-points. Thus, we need to determine a partition of the N individuals into a number k of groups, in such way that individuals in the same group are as alike as possible, but as distinct as possible from individuals in other groups. This method can be applied to endogenously identify k groups in income distributions: possible applications can be poverty

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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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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The Impact of prevention measures and organisational factors on occupational injuries

This paper analyses the impact of a series of managerial and organisational factors on occupational injuries. These consist of occupational safety measures, as regards both the intensity and the orientation of risk prevention in companies, and the adoption of certain work organisation practices, quality management and the use of flexible production technologies. We estimate a negative binomial regression based on a sample of 213 Spanish industrial establishments, defining a constant random parameter to take account of non-observable heterogeneity. Our results show that occupational safety measures, the intensive use of quality management tools and the empowerment of workers all help to reduce the number of injuries. We have also confirmed the presence of synergies between the organisational factors analysed and the development of an occupational safety strategy featuring participation and the extension of prevention to all levels of the organisation.

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.

Una universidad donde confluyen la educación, la investigación y la ciudadanía

El projecte de recerca s'ha basat en el projecte Miquel Martí i Pol, que ha consistit en la creació i manteniment d'un jardí dedicat a la memòria del poeta, amb persones en situació d'exclusió social (per motius de malaltia mental, immigració, pobresa) i estudiants de teràpia ocupacional de la Universitat de Vic, des d'una sinergia única entre la Universitat de Vic i institucions públiques, socials i empresarials. La recerca ve a cobrir la falta de coneixement sobre l'impacte terapèutic de la jardineria, com afirmava Sempik al 2003. Així mateix, genera coneixements sobre l'ocupació humana, la ciutadania, les comunitats inclusives, les aliances estratègiques i sobre noves praxis educatives en el marc del nou Espai Europeu d'Educació Superior (EEES). El marc teòric s'ha basat en una visió transdisciplinària, des de l'educació, la filosofia, la psicologia, la sociologia, la teràpia ocupacional, la política, l'ecologia i l'antropologia. S'ha desenvolupat una recerca inspirada per la investigació acció participativa que ha aprofundit en el significat que ha tingut aquesta experiència per a les persones implicades en el procés de creació del jardí: les persones procedents de col•lectius en situació d'exclusió, els estudiants, així com els representants de les institucions públiques, socials, empresarials i la pròpia Universitat de Vic. Així es van desenvolupar una sèrie d'entrevistes a fons i formularis amb 5 jardiners; 2 estudiants; la Consellera d'Acció Social de l'Ajuntament de Vic; el Conseller d'Acció Social del Consell Comarcal d'Osona; el President de Caritas; la terapeuta ocupacional de la Fundació Centre Mèdic Psicopedagògic d'Osona; la Rectora de la Universitat de Vic; la Directora de l'EUCS i el President del Rotary Club. Els temes que han sorgit en la recerca són: La construcció de l'ocupació significativa; la jardineria com a font de benestar; un espai de bellesa; la dignitat de la ciutadania; la creació de comunitats inclusives; una Universitat al servei de la Humanitat: noves praxis educatives; l'art de les aliances estratègiques i de les sinergies. Els coneixements generats tenen relació amb els estudis de teràpia ocupacional, així com per a educació social, infermeria, psicologia i ciències ambientals. A més a més són una aposta per al desenvolupament de noves praxis educatives en el nou EEES. El treball ha estat qualificat com a excel•lent per unanimitat del tribunal.

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

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Orbit decidability and the conjugacy problem for some extensions of groups

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