Browsing by Author "Martino, Armando"
Now showing items 110 of 10

A description of autofixed subgroups in a free group
Martino, Armando; Ventura Capell, Enric (200406)
Article
Open AccessLet F be a finitely generated free group. By using BestvinaHandel 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. (20161201)
Article
Open AccessWe 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 AccessLet 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 (20161116)
Article
Open AccessWe 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 automorphismfixed subgroups of a free group
Martino, Armando; Ventura Capell, Enric (200008)
Article
Open AccessLet F be a flnitely generated free group, and let n denote its rank. A subgroup H of F is said to be automorphismflxed, or autoflxed 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 policyWe 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 ... 
Probabilistic nilpotence in infinite groups
Ventura Capell, Enric; Martino, Armando; Tointon, Matthew C.H.; Valiunas, Motiejus (20210702)
Article
Open AccessThe ‘degree of kstep nilpotence’ of a finite group G is the proportion of the tuples (x1,…, xk+1 ¿ Gk+1 for which the simple commutator [x1, …, xk+1] is equal to the identity. In this paper we study versions of this for ... 
Statistical properties of subgroups of free groups
Bassino, Frederique; Martino, Armando; Nicaud, Cyril; Ventura Capell, Enric; Weil, Pascal (20130204)
Article
Open AccessThe usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the socalled wordbased distribution: subgroups are generated ... 
The automorphism group of a freebycyclic group in rank 2
Bogopolski, Oleg; Martino, Armando; Ventura Capell, Enric (200705)
Article
Open AccessLet ¡ 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 freebycyclic groups
Martino, Armando; Ventura Capell, Enric (200404)
Research report
Open AccessWe show that the conjugacy problem is solvable in [finitely generated free]bycyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed sub groups of free group ...