Exploració per tema "Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups"

Ara es mostren els items 1-20 de 26

    • A list of applications of stallings automata 

      Delgado Pin, Jordi; Ventura Capell, Enric (2022-11-22)
      Article
      Accés obert
      This survey is intended to be a fast (and reasonably updated) reference for the theory of Stallings automata and its applications to the study of subgroups of the free group, with the main accent on algorithmic aspects. ...

    • A recursive presentation for Mihailova's subgroup 

      Bogopolski, Oleg; Ventura Capell, Enric (2010)
      Article
      Accés obert
      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
      Accés obert
      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 ...

    • Algorithmic recognition of infinite cyclic extensions 

      Cavallo, Bren; Delgado Rodríguez, Jordi; Kahrobaei, Delaram; Ventura Capell, Enric (2016-10-25)
      Article
      Accés obert
      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)
      Projecte Final de Màster Oficial
      Accés obert
      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 ...

    • An irrational-slope Thompson’s group 

      Burillo Puig, José; Nucinkis, Brita; Reeves, Lawrence (2021-01-01)
      Article
      Accés obert
      The purpose of this paper is to study the properties of the irrational-slope Thompson’s group Ft introduced by Cleary in [11]. We construct presentations, both finite and infinite, and we describe its combinatorial structure ...

    • Banach Tarski Paradox and Amenability 

      Naranjo Barnet, Pol (Universitat Politècnica de Catalunya, 2015-02)
      Treball Final de Grau
      Accés obert
      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
      Accés obert
      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)
      Treball Final de Grau
      Accés obert
      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
      Accés obert
      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 ...

    • El grupo F de Thompson 

      Guardado Fuente, Rebeca (Universitat Politècnica de Catalunya, 2015-07)
      Treball Final de Grau
      Accés obert
      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)
      Projecte Final de Màster Oficial
      Accés obert
      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 ...

    • Finite automata for Schreier graphs of virtually free groups 

      Silva, Pedro V.; Soler Escrivà, Xaro; Ventura Capell, Enric (2016-01-01)
      Article
      Accés obert
      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 ...

    • Fixed subgroups are compressed in surface groups 

      Zhang, Qiang; Ventura Capell, Enric; Wu, Jianchun (2015-08-01)
      Article
      Accés obert
      For a compact surface Sigma (orientable or not, and with boundary or not), we show that the fixed subgroup, Fix B, of any family B of endomorphisms of pi(1)(Sigma) is compressed in pi(1)(Sigma), i.e. rk(Fix B) <= rk(H) for ...

    • Fixed subgroups in direct products of surface groups of Euclidean type 

      Wu, Jianchun; Ventura Capell, Enric; Zhang, Qiang (2020-02-24)
      Article
      Accés obert
      We give an explicit characterization of which direct products G of surface groups of Euclidean type satisfy that the fixed subgroup of any automorphism (or endomorphism) of G is compressed, and of which is it always inert.

    • Fixed subgroups in free groups: a survey 

      Ventura Capell, Enric (2002-03)
      Article
      Accés obert
      This note is a survey of the main results known about fixed subgroups of endomorphisms of finitely generated free groups. A historic point of view is taken, emphasizing the evolution of this line of research, from ...

    • Group-theoretic orbit decidability 

      Ventura Capell, Enric (De Gruytr, 2014-12-01)
      Article
      Accés obert
      A recent collection of papers in the last years have given a renovated interest to the notion of orbit decidability. This is a new quite general algorithmic notion, connecting with several classical results, and closely ...

    • Intersection configurations in free and free times free-abelian groups 

      Delgado Rodríguez, Jordi; Roy, Mallika; Ventura Capell, Enric (Cambridge University Press, 2023-09-11)
      Article
      Accés obert
      In this paper, we study intersection configurations – which describe the behaviour of multiple (finite) intersections of subgroups with respect to finite generability – in the realm of free and free times free-abelian ...

    • Intersection problem for Droms RAAGs 

      Delgado Rodríguez, Jorge; Ventura Capell, Enric; Zakharov, Alexander (2018-01-01)
      Article
      Accés obert
      We solve the subgroup intersection problem (SIP) for any RAAG G of Droms type (i.e., with defining graph not containing induced squares or paths of length 3): there is an algorithm which, given finite sets of generators ...

    • Irrational-slope versions of thompson's groups T and V 

      Burillo Puig, José; Nucinkis, Brita; Reeves, Lawrence (2022-02-11)
      Article
      Accés obert
      In this paper, we consider the T - and V -versions, Tt and Vt , of the irrational slope Thompson group Ft considered in J. Burillo, B. Nucinkis and L. Reeves [An irrational-slope Thompson's group, Publ. Mat. 65 (2021), ...