Exploració per tema "Group theory"
Ara es mostren els items 1-20 de 74
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A description of auto-fixed subgroups in a free group
(2004-06)
Article
Accés obertLet 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 list of applications of stallings automata
(2022-11-22)
Article
Accés obertThis 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
(2010)
Article
Accés obertWe 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
(2012-12-04)
Article
Accés obertThe 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
(Universitat Politècnica de Catalunya, 2020-07)
Projecte Final de Màster Oficial
Accés obertEs 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
(2013-10-01)
Article
Accés obertWe 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
(2016-10-25)
Article
Accés obertWe 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
(Universitat Politècnica de Catalunya, 2019-10)
Projecte Final de Màster Oficial
Accés obertAmenability 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
(2021-01-01)
Article
Accés obertThe 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 ... -
Autòmats de Stallings, un camí d'anada i tornada
(2022-12-14)
Article
Accés obertEn aquest article revisem algunes de les propietats fonamentals del grup lliure i fem una exposició detallada de la teoria dels autòmats de Stallings, una interpretació geomètrica dels seus subgrups que ha estat (i segueix ... -
Banach Tarski Paradox and Amenability
(Universitat Politècnica de Catalunya, 2015-02)
Treball Final de Grau
Accés obertThe 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
(2016-09-01)
Article
Accés obertFor 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
(Universitat Politècnica de Catalunya, 2015-07)
Treball Final de Grau
Accés obertEn 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
(Universidad de Almería, 2012)
Text en actes de congrés
Accés restringit per política de l'editorialUn 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
(2016-12-01)
Article
Accés obertWe 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
(2018-07-09)
Article
Accés obertIn [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
(2018-09-01)
Article
Accés obertFor 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
(2015)
Article
Accés obertLet 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
(2017-01-01)
Article
Accés obertFor 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 ... -
Counting subgroups using Stallings automata and generalizations
(Universitat Politècnica de Catalunya, 2023-09-12)
Projecte Final de Màster Oficial
Accés obertL'estudi dels subgrups del grup lliure es pot dur a terme utilitzant la teoria desenvolupada per Stallings, que dóna una representació gràfica que codifica les propietats algebraiques d'aquests subgrups en forma d'autòmats ...