The automorphism group of Thompson’s group $F$: subgroups and metric properties
نویسندگان
چکیده
منابع مشابه
The Automorphism Group of Thompson’s Group F : Subgroups and Metric Properties
We describe some of the geometric properties of the automorphism group Aut(F ) of Thompson’s group F . We give realizations of Aut(F ) geometrically via periodic tree pair diagrams, which lead to natural presentations and give effective methods for estimating the word length of elements. We study some natural subgroups of Aut(F ) and their metric properties. In particular, we show that the subg...
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Let n ≥ 2 and Fn be the free group of rank n. Its automorphism group Aut(Fn) has a well-known surjective linear representation ρ : Aut(Fn) −→ Aut(Fn/F ′ n) = GLn(Z) where F ′ n denotes the commutator subgroup of Fn. By Aut (Fn) := ρ(SLn(Z)) we denote the special automorphism group of Fn. For an epimorphism π : Fn → G of Fn onto a finite group G we call Γ(G, π) := {φ ∈ Aut(Fn) | πφ = π} the stan...
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We consider random subgroups of Thompson’s group F with respect to two natural stratifications of the set of all k generator subgroups of this group. We find that the isomorphism classes of subgroups which occur with positive density vary greatly between the two stratifications. We give the first known examples of persistent subgroups, whose isomorphism classes occur with positive density withi...
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ژورنال
عنوان ژورنال: Revista Matemática Iberoamericana
سال: 2013
ISSN: 0213-2230
DOI: 10.4171/rmi/741