Now showing items 1-9 of 9

    • Amenability and Thompson’s group F 

      Acedo Moscoso, Diego (Universitat Politècnica de Catalunya, 2019-10)
      Master thesis
      Open Access
      Amenability is a group theoretical property consisting in the existence of a finite measure defined on all subsets of the group. The concept is motivated and introduced, and some criteria, characterizations and generalizations ...
    • Banach Tarski Paradox and Amenability 

      Naranjo Barnet, Pol (Universitat Politècnica de Catalunya, 2015-02)
      Bachelor thesis
      Open Access
      The main objective of this bachelor thesis is to prove Banach-Tarski theorem. The theorem states that a ball in a 3-dimensional space can be split into finitely many pieces that can be rearranged to form two balls, each ...
    • Calculadora para el retículo de subgrupos del grupo libre 

      García Gómez, Ángel (Universitat Politècnica de Catalunya, 2015-07)
      Bachelor thesis
      Open Access
      En este trabajo se describen algunas propiedades y operaciones básicas del grupo libre y de sus subgrupos, así como una metodología para la resolución algorítmica de ciertos problemas algebraicos mediante el uso de grafos. ...
    • Commutators in groups of piecewise projective homeomorphisms 

      Burillo Puig, José; Lodha, Yash; Reeves, Lawrence (2018-07-09)
      Article
      Open Access
      In [7] Monod introduced examples of groups of piecewise projective homeomorphisms which are not amenable and which do not contain free subgroups, and in [6] Lodha and Moore introduced examples of finitely presented groups ...
    • Degree of commutativity of infinite groups 

      Antolin, Yago; Martino, Armando; Ventura Capell, Enric (2016-11-16)
      Article
      Open Access
      We prove that, in a finitely generated residually finite group of subexponential growth, the proportion of commuting pairs is positive if and only if the group is virtually abelian. In particular, this covers the case where ...
    • El grupo F de Thompson 

      Guardado Fuente, Rebeca (Universitat Politècnica de Catalunya, 2015-07)
      Bachelor thesis
      Open Access
      El tema principal de este trabajo es la introducción del grupo F de Thompson, que fue definido el 1965 por Richard Thompson. Nuestro objetivo principal es el estudio del grupo F de Thompson, partiendo de su definición y ...
    • Grups de simetria del pla i aplicacions 

      Julià Verdaguer, Anna (Universitat Politècnica de Catalunya, 2014-07)
      Bachelor thesis
      Open Access
      L'objectiu d'aquest treball és estudiar i classificar els 17 grups de simetria que existeixen en el pla euclidià. El que es fa és utilitzar coneixements ja adquirits al llarg de la carrera, en assignatures com Geometria ...
    • Statistical properties of subgroups of free groups 

      Bassino, Frederique; Martino, Armando; Nicaud, Cyril; Ventura Capell, Enric; Weil, Pascal (2013-02-04)
      Article
      Open Access
      The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated ...
    • The Grigorchuk group and groups of intermediate growth 

      Pérez Pérez, Aitor (Universitat Politècnica de Catalunya, 2015-07)
      Master thesis
      Open Access
      En aquest treball es fa una introducció al creixement en grups, donant la definició, algunes propietats i exemples. Es presenta el grup de Grigorchuk G com a subgrup dels automorfismes de l'arbre binary infinit, i es prova ...