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N. A. Gusevskiî 《Siberian Mathematical Journal》1996,37(1):79-93
Conclusion M. Freedman and R. Skora proved that the groups they constructed in [2, 3] have extensions toS
4, and that these extensions are conjugate with Schottky groups in the homeomorphism group ofS
4.Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 37, No. 1, pp. 90–107, January–February, 1996. 相似文献
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N. A. Shirokov 《Journal of Mathematical Sciences》1998,92(1):3675-3684
Let Γ be a geometrically finite or a quasi-Fuchsian Kleiman group such that ∞ ? $\mathop \Omega \limits^o \left( v \right)$ . We establish the relation $X = clos_X L\left( {\frac{1}{{1 - a}},a \in \Xi } \right)$ for some countable sets Ξ?ω(Γ) connected with actions of elements of Γ, and for the space X=C(Γ) or for the Hölder classes X=Lα(Λ), 0<α<1, where Λ=Λ(Γ)=?\Ω is the limit set of Γ. Bibliography: 6 titles. 相似文献
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L. D. Potyagailo 《Siberian Mathematical Journal》1989,30(5):773-783
Dedicated to Yurii Grigor'evich Reshetnyak on his sixtieth birthday. 相似文献
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Luis Paris 《Proceedings of the American Mathematical Society》1997,125(3):731-738
Let be a Coxeter system, and let be a subset of . The subgroup of generated by is denoted by and is called a parabolic subgroup. We give the precise definition of the commensurator of a subgroup in a group. In particular, the commensurator of in is the subgroup of in such that has finite index in both and . The subgroup can be decomposed in the form where is finite and all the irreducible components of are infinite. Let be the set of in such that for all . We prove that the commensurator of is . In particular, the commensurator of a parabolic subgroup is a parabolic subgroup, and is its own commensurator if and only if .
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V. V. Korableva 《Algebra and Logic》2010,49(3):246-255
Ranks, degrees, subdegrees, and double stabilizers of permutation representations for finite symplectic groups are defined
on cosets with respect to maximal parabolic subgroups. 相似文献
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In [Thompson, J., 1968, Non-solvable finite groups all of whose local subgroups are solvable. Bulletin of the American Mathematical Society, 74, 383–437.], Thompson showed that a finite group G is solvable if and only if every two-generated subgroup is solvable (Corollary 2, p. 388). Recently, Grunevald et al. [Grunewald et al., 2000, Two-variable identities in groups and Lie algebras. Rossiiskaya Akademiya Nauk POMI, 272, 161–176; 2003. Journal of Mathematical Sciences (New York), 116, 2972–2981.] have shown that the analogue holds for finite-dimensional Lie algebras over infinite fields of characteristic greater than 5. It is a natural question to ask to what extent the two-generated subalgebras determine the structure of the algebra. It is to this question that this article is addressed. Here, we consider the classes of strongly-solvable and of supersolvable Lie algebras, and the property of triangulability. 相似文献
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Indranil Biswas Carlos Florentino Sean Lawton Marina Logares 《Geometriae Dedicata》2014,168(1):143-159
Let $G$ be a complex affine algebraic reductive group, and let $K\,\subset \, G$ be a maximal compact subgroup. Fix h $\,:=\,(h_{1}\,,\ldots \,,h_{m})\,\in \, K^{m}$ . For $n\, \ge \, 0$ , let $\mathsf X _{\mathbf{{h}},n}^{G}$ (respectively, $\mathsf X _{\mathbf{{h}},n}^{K}$ ) be the space of equivalence classes of representations of the free group on $m+n$ generators in $G$ (respectively, $K$ ) such that for each $1\le i\le m$ , the image of the $i$ -th free generator is conjugate to $h_{i}$ . These spaces are parabolic analogues of character varieties of free groups. We prove that $\mathsf X _{\mathbf{{h}},n}^{K}$ is a strong deformation retraction of $\mathsf X _{\mathbf{{h}},n}^{G}$ . In particular, $\mathsf X _{\mathbf{{h}},n}^{G}$ and $\mathsf X _{\mathbf{{h}},n}^{K}$ are homotopy equivalent. We also describe explicit examples relating $\mathsf X _{\mathbf{{h}},n}^{G}$ to relative character varieties. 相似文献
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Simon Goodwin 《Indagationes Mathematicae》2004,15(2):189-207
Let G be a reductive linear algebraic group, P a parabolic subgroup of G and Pu its unipotent radical. We consider the adjoint action of P on the Lie algebra u of Pu. Each higher term u(l) of the descending central series of u is stable under this action. For classical G all instances when P acts on u(l) with a finite number of orbits were determined in [9], [10], [3] and [4]. In this note we extend these results to groups of type F4 and E6. Moreover, when P acts on u(l) with an infinite number of orbits, we determine whether P still acts with a dense orbit. For G of type E7 and E8 we investigate only the case of a Borel subgroup.We present a complete classification of all instances when u(l) is a prehomogeneous space for a Borel subgroup B of a reductive algebraic group for any l ≥ 0. 相似文献
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Huiling Li 《Journal of Combinatorial Theory, Series A》2009,116(1):1-11
Suppose that an almost simple group G acts line transitively on a finite linear space S. Let Gx be a point stabilizer in G and suppose that G has socle T, a simple group of Lie type. In this paper we show that if T∩Gx is a parabolic subgroup of T, then G is flag transitive on S. 相似文献