Twisted first homology groups of the automorphism group of a free group
نویسندگان
چکیده
منابع مشابه
Twisted Second Homology Groups of the Automorphism Group of a Free Group
In this paper, we compute the second homology groups of the automorphism group of a free group with coefficients in the abelianization of the free group and its dual group except for the 2-torsion part, using combinatorial group theory.
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H"{o}lder in 1893 characterized all groups of order $pqr$ where $p>q>r$ are prime numbers. In this paper, by using new presentations of these groups, we compute their full automorphism group.
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We compute a twisted first cohomology group of the automorphism group of a free group with coefficients in the abelianization V of the IA-automorphism group of a free group. In particular, we show that it is generated by two crossed homomorphisms constructed with the Magnus representation and the Magnus expansion due to Morita and Kawazumi respectively. As a corollary, we see that the first Joh...
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متن کاملCongruence 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...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2006
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2005.05.001