Now showing items 1-20 of 58

    • A description of auto-fixed subgroups in a free group 

      Martino, Armando; Ventura Capell, Enric (2004-06)
      Article
      Open Access
      Let F be a finitely generated free group. By using Bestvina-Handel theory, as well as some further improvements, the eigengroups of a given automorphism of F (and its fixed subgroup among them) are globally analyzed and ...
    • A recursive presentation for Mihailova's subgroup 

      Bogopolski, Oleg; Ventura Capell, Enric (2010)
      Article
      Open Access
      We give an explicit recursive presentation for Mihailova's sub- group M(H) of Fn Fn corresponding to a nite, concise and Pei er aspherical presentation H = hx1; : : : ; xn jR1; : : : ;Rmi. This partially answers a ...
    • A Whitehad algorithm for toral relatively hyperbolic groups 

      Kharlampovich, Olga; Ventura Capell, Enric (2012-12-04)
      Article
      Open Access
      The Whitehead problem is solved in the class of toral relatively hyperbolic groups G (i.e. torsion-free relatively hyperbolic groups with abelian parabolic subgroups): there is an algorithm which, given two nite ...
    • Algebraic extensions in free groups and Stallings graphs 

      Mijares Verdú, Sebastià (Universitat Politècnica de Catalunya, 2020-07)
      Master thesis
      Open Access
      Es realitza un estudi de les extensions algebraiques de subgrups lliures, fent ús extensiu dels grafs de Stallings, en àmbits com la sobrejectivitat de morfismes entre grafs de Stallings, o el comportament d'aquestes com ...
    • Algorithmic problems for free-abelian times free groups 

      Delgado Rodríguez, Jordi; Ventura Capell, Enric (2013-10-01)
      Article
      Open Access
      We study direct products of free-abelian and free groups with special emphasis on algorithmic problems. After giving natural extensions of standard notions into that family, we find an explicit expression for an arbitrary ...
    • Algorithmic recognition of infinite cyclic extensions 

      Cavallo, Bren; Delgado Rodríguez, Jordi; Kahrobaei, Delaram; Ventura Capell, Enric (2016-10-25)
      Article
      Open Access
      We prove that one cannot algorithmically decide whether a finitely presented Z-extension admits a finitely generated base group, and we use this fact to prove the undecidability of the BNS invariant. Furthermore, we show ...
    • 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 ...
    • Bounding the gap between a free group (outer) automorphism and its inverse 

      Ladra, Manuel; Silva, Pedro V.; Ventura Capell, Enric (2016-09-01)
      Article
      Open Access
      For any finitely generated group GG , two complexity functions aGaG and ßGßG are defined to measure the maximal possible gap between the norm of an automorphism (respectively, outer automorphism) of GG and the norm ...
    • 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. ...
    • Clasificación de 3-semigrupos numéricos mediante L-formas 

      Aguiló Gost, Francisco de Asis L.; Marijuan López, Carlos (Universidad de Almería, 2012)
      Conference report
      Restricted access - publisher's policy
      Un semigrupo num erico generado por tres elementos tiene asociadas una o dos teselaciones peri odicas del plano generadas por una baldosa en forma de L. Se conocen algunas propiedades combinatorias del semigrupo en t ...
    • Commensurations and metric properties of Houghton's groups 

      Burillo Puig, José; Cleary, Sean; Martino, Armando; Röver, Claas E. (2016-12-01)
      Article
      Open Access
      We describe the automorphism groups and the abstract commensurators of Houghton’s groups. Then we give sharp estimates for the word metric of these groups and deduce that the commensurators embed into the corresponding ...
    • 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 ...
    • Computation of numerical semigroups by means of seeds 

      Bras Amorós, Maria; Fernández González, Julio (2018-09-01)
      Article
      Open Access
      For the elements of a numerical semigroup which are larger than the Frobenius number, we introduce the definition of seed by broadening the notion of generator. This new concept allows us to explore the semigroup tree in ...
    • Conjugacy in houghton's groups 

      Antolin, Yago; Burillo Puig, José; Martino, Armando (2015)
      Article
      Open Access
      Let n ∈ N. Houghton’s group Hn is the group of permutations of {1, . . . , n} × N, that eventually act as a translation in each copy of N. We prove the solvability of the conjugacy problem and conjugator search problem for ...
    • Constraints on the automorphism group of a curve 

      González Rovira, Josep (2017-01-01)
      Article
      Open Access
      For a curve of genus > 1 defined over a finite field, we present a sufficient criterion for the non-existence of automorphisms of order a power of a rational prime. We show how this criterion can be used to determine the ...
    • 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 ...
    • Extensions de l'algorisme clàssic de Whitehead 

      Balle Pigem, Borja de (Universitat Politècnica de Catalunya, 2009-02)
      Master thesis
      Open Access
      L'algoritme clàssic de Whitehead decideix si dues paraules del grup lliure pertanyen o no a la mateixa òrbita per l'acció del grup d'automorfismes. La demostració clàssica és molt combinatòrica i tècnica (i desagradable ...
    • Extensions of groups 

      Ruiz Herrero, Víctor (Universitat Politècnica de Catalunya, 2018-07)
      Bachelor thesis
      Open Access
      A study of extensions of groups: given 2 groups G and K, I study the groups E that have K as a normal subgroup such that G = E/K. It is related with exact sequences and group cohomology.