Now showing items 1-9 of 9

    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • On automorphism-fixed subgroups of a free group 

      Martino, Armando; Ventura Capell, Enric (2000-08)
      Article
      Open Access
      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 ...
    • On two distributions of subgroups of free groups 

      Bassino, Frédérique; Martino, Armando; Nicaud, Cyril; Ventura Capell, Enric; Weil, Pascal (Society for Industrial and Applied Mathematics, 2010)
      Conference report
      Restricted access - publisher's policy
      We study and compare two natural distributions of finitely generated subgroups of free groups. One is based on the random generation of tuples of reduced words; that is the one classically used by group theorists. The ...
    • Statistical properties of subgroups of free groups 

      Bassino, Frederique; Martino, Armando; Nicaud, Cyril; Ventura Capell, Enric; Weil, Pascal (2013-02-04)
      Article
      Open Access
      The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated ...
    • The automorphism group of a free-by-cyclic group in rank 2 

      Bogopolski, Oleg; Martino, Armando; Ventura Capell, Enric (2007-05)
      Article
      Open Access
      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)
      External research report
      Open Access
      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 ...