The automorphism group of a free group is not linear
نویسندگان
چکیده
منابع مشابه
Congruence Subgroups of the Automorphism Group of a Free Group
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...
متن کاملThe Automorphism Tower of a Free Group
We prove that the automorphism group of any non-abelian free group F is complete. The key technical step in the proof: the set of all conjugations by powers of primitive elements is first-order parameter-free definable in the group Aut(F ). Introduction In 1975 J. Dyer and E. Formanek [2] had proved that the automorphism group of a finitely generated non-abelian free group F is complete (that i...
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It is proved that the automorphism-group of a countable structure cannot be a free uncountable groupi. The idea is that instead proving that every countable set of equations of a certain form has a solution, we prove that this holds for a co-meagre family of appropriate countable sets of equations. Can a countable structure have an automorphism group, which a free uncountable group? This was a ...
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In this paper, we show that the abelianization of the kernel of the Magnus representation of the automorphism group of a free group is not finitely generated.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1992
ISSN: 0021-8693
DOI: 10.1016/0021-8693(92)90029-l