Exploració per tema "Free groups"

Ara es mostren els items 1-13 de 13

    • Algorithmic problems about subgroups of free groups 

      Santamaría García, Guillermo (Universitat Politècnica de Catalunya, 2013-09)
      Treball Final de Grau
      Accés obert
      The study of the lattice of subgroups of $F_{k}$ changed completely when J.Stallings published a paper that developed some special graphs in order to solve several algorithmic problems about subgroups like the membership ...

    • Algorithmic problems for free-abelian times free groups 

      Delgado Rodríguez, Jordi; Ventura Capell, Enric (2013-10-01)
      Article
      Accés obert
      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 ...

    • 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 ...

    • Degrees of compression and inertia for free-abelian times free groups 

      Roy, Mallika; Ventura Capell, Enric (Elsevier, 2021-02-15)
      Article
      Accés obert
      We introduce the concepts of degree of inertia, diG(H), and degree of compression,dcG(H), of a finitely generated subgroupHof a given groupG. For the case of direct productsof free-abelian and free groups, we compute the ...

    • 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 ...

    • 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 ...

    • On automorphism-fixed subgroups of a free group 

      Martino, Armando; Ventura Capell, Enric (2000-08)
      Article
      Accés obert
      Let F be a flnitely generated free group, and let n denote its rank. A subgroup H of F is said to be automorphism-flxed, or auto-flxed for short, if there exists a set S of automorphisms of F such that H is precisely the ...

    • Product-free sets in the free group 

      Ortega Sánchez Colomer, Miquel; Rué Perna, Juan José; Serra Albó, Oriol (2023)
      Comunicació de congrés
      Accés obert
      We prove that product-free sets of the free group over a finite alphabet have max-imum density1/2with respect to the natural measure that assigns total weight oneto each set of irreducible words of a given length. This ...

    • The automorphism group of a free-by-cyclic group in rank 2 

      Bogopolski, Oleg; Martino, Armando; Ventura Capell, Enric (2007-05)
      Article
      Accés obert
      Let ¡ be an automorphism of a free group F 2 of rank 2 and let M ¡ = F 2 o ¡ Z be the corresponding mapping torus of ¡ . We prove that the group Out ( M ¡ ) is usually virtually cyclic. More- over, ...

    • The conjugacy problem for free-by-cyclic groups 

      Martino, Armando; Ventura Capell, Enric (2004-04)
      Report de recerca
      Accés obert
      We show that the conjugacy problem is solvable in [finitely generated free]-by-cyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed sub- groups of free group ...

    • The design of a parallel algorithm to solve the word problem for the free partially commutative groups 

      Gabarró Vallès, Joaquim (1991-10-15)
      Report de recerca
      Accés obert
      We develop a parallel algorithm to solve the word problem for free partially commutative groups. These groups were introduced by C. Wrathall to generalize free groups. We represent the elements of these groups as a certain ...