共查询到20条相似文献,搜索用时 0 毫秒
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S. Andreadakis 《Archiv der Mathematik》1979,32(1):227-233
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Takao Satoh 《Journal of Algebra》2010,323(12):3182-3201
In this paper we consider the Johnson homomorphism of the automorphism group of a free group with respect to the lower central series of the IA-automorphism group of a free group. In particular, we determine the rational cokernel of the fourth Johnson homomorphism, and show that there appears a new obstruction for the surjectivity of the Johnson homomorphism. Furthermore we characterize this obstruction using trace maps. 相似文献
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Gábor Tardos 《Inventiones Mathematicae》1992,108(1):29-36
Summary The Hanna Neumann Conjecture says that the intersection of subgroups of rankn+1 andm+1 of a free group has rank at mostnm+1. This paper proves the conjecture for the casem=1. (See Theorem 1.) Our methods imply that the strengthened Hanna Neumann Conjecture is also true in this case (Theorem 2).Oblatum 31-V-1991 & 8-X-1991 相似文献
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The automorphism group AutFn of a free group Fn of rank n acts on the product of n copies of a group G by substituting n elements of G into the words defining an automorphism of the free group. This gives rise to an antihomomorphism from AutFnto a permutation group. We determine this antihomomorphic image of AutFn when G is the semidirect product Zp x Zq 相似文献
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Emmanuel Breuillard Ben Green Robert Guralnick Terence Tao 《Israel Journal of Mathematics》2012,192(1):347-379
We show that (with one possible exception) there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski dense. As a consequence, we get new generating results for finite simple groups of Lie type and a strengthening of a theorem of Borel related to the Hausdorff-Banach-Tarski paradox. In a sequel to this paper, we use this result to also establish uniform expansion properties for random Cayley graphs over finite simple groups of Lie type 相似文献
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S.M. Gersten 《Journal of Pure and Applied Algebra》1984,33(3):269-279
A presentation is given for SAn, the group of automorphisms of determinant 1 of a free group Fn of rank n. The canonical isomorphisms are established for n ≥ 5, where An is the full group of automorphisms of Fn. 相似文献
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M. Rovinsky 《Selecta Mathematica, New Series》2009,15(2):343-376
Let G be the automorphism group of an extension of algebraically closed fields of characteristic zero of transcendence degree n, 1 ≤ n ≤ ∞. In this paper we
The study of open subgroups is motivated by the study of (the stabilizers of) smooth representations undertaken in [R1, R3].
The functor Γ is an analogue of the global sections functor on the category of sheaves on a smooth proper algebraic variety.
Another result is that ‘interesting’ semilinear representations are ‘globally generated’.
相似文献
• | construct some maximal closed non-open subgroups Gv, and some (all, in the case of countable transcendence degree) maximal open proper subgroups of G; |
• | describe, in the case of countable transcendence degree, the automorphism subgroups over the intermediate subfields (a question of Krull, [K2, §4, question 3b)]); |
• | construct, in the case n = ∞, a fully faithful subfunctor ( − )v of the forgetful functor from the category of smooth representations of G to the category of smooth representations of Gv; |
• | construct, using the functors ( − )v, a subfunctor Γ of the identity functor on , coincident (via the forgetful functor) with the functor Γ on the category of admissible semilinear representations of G constructed in [R3] in the case n = ∞ and . |
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Takao Satoh 《Journal of Pure and Applied Algebra》2007,211(2):547-565
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. 相似文献
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Takao Satoh 《Journal of Pure and Applied Algebra》2006,204(2):334-348
The automorphism group and outer automorphism group of a free group Fn of rank n act on the abelianized group H of Fn and the dual group H* of H. The twisted first homology groups of and with coefficients in H and H* are calculated. 相似文献
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Koji Fujiwara 《Israel Journal of Mathematics》2002,131(1):277-284
LetG be a one-ended, word-hyperbolic group. Let Γ be an irreducible lattice in a connected semi-simple Lie group of rank at least
2. Ifh: Γ→Out(G) is a homomorphism, then Im(h) is finite.
Dedicated to Professor Takushiro Ochiai for his sixtieth birthday 相似文献
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It is shown that H = Γ(T)v is normal in G = Γ(Tv) for any tree T and any vertex v, if and only if, for all vertices u in the neighborhood N of v, the set of images of u under G is either contained in N or has precisely the vertex u in common with N and every vertex in the set of images is fixed by H. Further, if S is the smallest normal subgroup of G containing H then is the direct product of the wreath products of various symmetric groups around groups of order 1 or 2. The degrees of the symmetric groups involved depend on the numbers of isomorphic components of Tv and the structure of such components. 相似文献
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J.G. Horne 《Linear algebra and its applications》1978,21(2):111-121
Let V be a real finite dimensional vector space, and let C be a full cone in C. In Sec. 3 we show that the group of automorphisms of a compact convex subset of V is compact in the uniform topology, and relate the group of automorphisms of C to the group of automorphisms of a compact convex cross-section of C. This section concludes with an application which generalizes the result that a proper Lorentz transformation has an eigenvector in the light cone. In Sec. 4 we relate the automorphism group of C to that of its irreducible components. In Sec. 5 we show that every compact group of automorphisms of C leaves a compact convex cross-section invariant. This result is applied to show that if C is a full polyhedral cone, then the automorphism group of C is the semidirect product of the (finite) automorphism group of a polytopal cross-section and a vector group whose dimension is equal to the number of irreducible components of C. An example shows that no such result holds for more general cones. 相似文献
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