1965
DOI: 10.1112/plms/s3-15.1.239
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On the Automorphisms of Free Groups and Free Nilpotent Groups

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Cited by 162 publications
(281 citation statements)
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“…(3) Are the groups Cb k n , k ≥ 1 is the subgroup of Aut(F n ), which consists of automorphisms acting trivially modulo the k-th term of the lower central series of F n . This chain was introduced in [1]. For which k ≥ 3, n ≥ 3 the groups IA k n are non-linear?…”
Section: Questionsmentioning
confidence: 99%
“…(3) Are the groups Cb k n , k ≥ 1 is the subgroup of Aut(F n ), which consists of automorphisms acting trivially modulo the k-th term of the lower central series of F n . This chain was introduced in [1]. For which k ≥ 3, n ≥ 3 the groups IA k n are non-linear?…”
Section: Questionsmentioning
confidence: 99%
“…Also, the homomorphism Aut(F n ) → Aut(F n /γ 3 (F n )), determined by the natural homomorphism F n → F n /γ 3 (F n ), is surjective [1] (equivalently, one says that the automorphism groups of finitely generated free nilpotent groups of class two are tame). It follows that in the automorphism group of any infinitely generated free nilpotent group of class two all finitary IA-automorphisms are contained in the normal closure of any analogue of K 12 .…”
Section: Stabilizing Everythingmentioning
confidence: 99%
“…The group π has lower central series defined recursively by Γ 0 = π and Γ k+1 = [π, Γ k ] for k ≥ 0, where the bracket of two groups denotes their commutator group, and the k-th nilpotent quotient is defined as N k = π/Γ k . Thus, we have the exact sequence (1) 0−→Γ k /Γ k+1 −→N k+1 −→N k −→1…”
Section: Introductionmentioning
confidence: 99%
“…If ϕ ∈ M g, * acts trivially on N k and γ ∈ N k+1 , then ϕ(γ)γ −1 ∈ Ker(N k+1 →N k ), so by exactness of (1) together with a few arguments, there are mappings τ k : I g, * (k)−→Hom(N k+1 , Γ k /Γ k+1 ), and these are called the Johnson homomorphisms introduced in [13] [14] (see also prior works of Andreadakis [1] and Sullivan [39]). See [14] for a survey of the Torelli groups and [28][31] [32] for further results.…”
Section: Introductionmentioning
confidence: 99%