Now showing items 1-20 of 53

  • 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 ...
  • 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 ...
  • 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 ...
  • 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
    Restricted access - publisher's policy
    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.
  • Familias infinitas de digrafos de Cayley de grado 2 óptimos sobre grupos abelianos finitos 

    Aguiló Gost, Francisco de Asis L.; Miralles de la Asunción, Alicia (Universidad de Almería, 2012)
    Conference report
    Restricted access - publisher's policy
    Sea GN un grupo abeliano finito de orden N. Para cada conjunto de generadores f, g = GN, consideremos el digrafo de Cayley Cay(GN, {f, g}). Seg´un sea GN c´ıclico o no c´ıclico, podemos obtener un di´ametro ´optimo ...
  • Finite automata for Schreier graphs of virtually free groups 

    Silva, Pedro V.; Soler Escrivà, Xaro; Ventura Capell, Enric (2016-01-01)
    Article
    Open Access
    The Stallings construction for f.g. subgroups of free groups is generalized by introducing the concept of Stallings section, which allows efficient computation of the core of a Schreier graph based on edge folding. It is ...