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1.
Let S be a closed Riemann surface of genus g. It is well known that there are Schottky groups producing uniformizations of S (Retrosection Theorem). Moreover, if τ: S → S is a conformal involution, it is also known that there is a Kleinian group K containing, as an index two subgroup, a Schottky group G that uniformizes S and so that K/G induces the cyclic group 〈τ〉. Let us now assume S is a stable Riemann surface and τ: S → S is a conformal involution. Again, it is known that S can be uniformized by a suitable noded Schottky group, but it is not known whether or not there is a Kleinian group K, containing a noded Schottky group G of index two, so that G uniformizes S and K/G induces 〈τ〉. In this paper we discuss this existence problem and provide some partial answers: (1) a complete positive answer for genus g ≤ 2 and for the case that S/〈τ〉 is of genus zero; (2) the existence of a Kleinian group K uniformizing the quotient stable Riemann orbifold S/〈τ〉. Applications to handlebodies with orientation-preserving involutions are also provided.  相似文献   

2.
If a finitely presented groupG is negatively curved, automatic or asynchronously automatic thenG has an asynchronously bounded “almost prefix closed” combing. Results in [Br1] and [E] imply that the fundamental group of any closed 3-manifold satisfying Thurston's geometrization conjecture has an asynchronously bounded, almost prefix closed combing. MAIN THEOREM. IfM is a compactP 2-irreducible 3-manifold,π 1 (M) has an asynchronously bounded, almost prefix closed combing, andH, a subgroup ofπ 1 (M), is quasiconvex with respect to this combing, then the cover ofM corresponding toH is a missing boundary manifold.  相似文献   

3.
Let G(OS)\mathbf{G}(\mathcal{O}_{S}) be an S-arithmetic subgroup of a connected, absolutely almost simple linear algebraic group G over a global function field K. We show that the sum of local ranks of G determines the homological finiteness properties of G(OS)\mathbf{G}(\mathcal{O}_{S}) provided the K-rank of G is 1. This shows that the general upper bound for the finiteness length of G(OS)\mathbf{G}(\mathcal{O}_{S}) established in an earlier paper is sharp in this case.  相似文献   

4.
Let K be a field and S=K[x 1,…,x n ]. In 1982, Stanley defined what is now called the Stanley depth of an S-module M, denoted sdepth (M), and conjectured that depth (M)≤sdepth (M) for all finitely generated S-modules M. This conjecture remains open for most cases. However, Herzog, Vladoiu and Zheng recently proposed a method of attack in the case when M=I/J with JI being monomial S-ideals. Specifically, their method associates M with a partially ordered set. In this paper we take advantage of this association by using combinatorial tools to analyze squarefree Veronese ideals in S. In particular, if I n,d is the squarefree Veronese ideal generated by all squarefree monomials of degree d, we show that if 1≤dn<5d+4, then sdepth (I n,d )=⌊(nd)/(d+1)⌋+d, and if d≥1 and n≥5d+4, then d+3≤sdepth (I n,d )≤⌊(nd)/(d+1)⌋+d.  相似文献   

5.
A subgroup H of a group G is said to be M-supplemented in G if there exists a subgroup B of G such that G = HB and T B < G for every maximal sub-group T of H. Moreover, a subgroup H is called c-supplemented in G if there exists a subgroup K such that G = HK and HKH G where H G is the largest normal subgroup of G contained in H. In this paper we give some conditions of supersolv-ability of finite group under assumption that some primary subgroups have some kinds of supplements, which are generalizations of some recent results.  相似文献   

6.
LetG be a connected semi-simple Lie group with finite center andSG a subsemigroup with interior points. LetG/L be a homogeneous space. There is a natural action ofS onG/L. The relationxy ifySx, x, yG/L, is transitive but not reflexive nor symmetric. Roughly, a control set is a subsetDG/L, inside of which reflexivity and symmetry for ≤ hold. Control sets are studied inG/L whenL is the minimal parabolic subgroup. They are characterized by means of the Weyl chambers inG meeting intS. Thus, for eachwW, the Weyl group ofG, there is a control setD w .D 1 is the only invariant control set, and the subsetW(S)={w:D w =D 1} turns out to be a subgroup. The control sets are determined byW(S)/W. The following consequences are derived: i)S=G ifS is transitive onG/H, i.e.Sx=G/H for allxG/H. HereH is a non discrete closed subgroup different fromG andG is simple. ii)S is neither left nor right reversible ifS #G iii)S is maximal only if it is the semigroup of compressions of a subset of some minimal flag manifold. Research partially supported by CNPq grant no 50.13.73/91-8  相似文献   

7.
LetK be the kernel of an epimorphismG→ℤ, whereG is a finitely presented group. IfK has infinitely many subgroups of index 2,3 or 4, then it has uncountably many. Moreover, ifK is the commutator subgroup of a classical knot groupG, then any homomorphism fromK onto the symmetric groupS 2 (resp. ℤ3) lifts to a homomorphism ontoS 3 (resp. alternating groupA 4). Both authors partially supported by NSF grants DMS-0071004 and DMS-0304971.  相似文献   

8.
Let M be a projective manifold, p: M G M a regular covering over M with a free Abelian transformation group G. We describe the holomorphic functions on M G of an exponential growth with respect to the distance defined by a metric pulled back from M. As a corollary, we obtain Cartwright and Liouville-type theorems for such functions. Our approach brings together the L 2 cohomology technique for holomorphic vector bundles on complete Kähler manifolds and the geometric properties of projective manifolds.  相似文献   

9.
We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup K of G such that G = HK and HK ⩽ core(H). In this paper it is proved that a finite group G is p-nilpotent if G is S 4-free and every minimal subgroup of PG N is c-supplemented in N G (P), and when p = 2 P is quaternion-free, where p is the smallest prime number dividing the order of G, P a Sylow p-subgroup of G. As some applications of this result, some known results are generalized.  相似文献   

10.
LetG be a connected, simply-connected, real semisimple Lie group andK a maximal compactly embedded subgroup ofG such thatD=G/K is a hermitian symmetric space. Consider the principal fiber bundleM=G/K s G/K, whereK s is the semisimple part ofK=K s ·Z K 0 andZ K 0 is the connected center ofK. The natural action ofG onM extends to an action ofG 1=G×Z K 0 . We prove as the main result thatM is weakly symmetric with respect toG 1 and complex conjugation. In the case whereD is an irreducible classical bounded symmetric domain andG is a classical matrix Lie group under a suitable quotient, we provide an explicit construction ofM=D×S 1 and determine a one-parameter family of Riemannian metrics onM invariant underG 1. Furthermore,M is irreducible with respect to . As a result, this provides new examples of weakly symmetric spaces that are nonsymmetric, including those already discovered by Selberg (cf. [M]) for the symplectic case and Berndt and Vanhecke [BV1] for the rank-one case.Research partially supported by an NSF grant. The author wishes to thank the International Erwin Schroedinger Institute for its hospitality during the preparation of this paper.  相似文献   

11.
Ki-perfect graphs are a special instance of F - G perfect graphs, where F and G are fixed graphs with F a partial subgraph of G. Given S, a collection of G-subgraphs of graph K, an F - G cover of S is a set of T of F-subgraphs of K such that each subgraph in S contains as a subgraph a member of T. An F - G packing of S is a subcollection S′? S such that no two subgraphs in S′ have an F-subgraph in common. K is F - G perfect if for all such S, the minimum cardinality of an F - G cover of S equals the maximum cardinality of an F - G packing of S. Thus Ki-perfect graphs are precisely Ki-1 - Ki perfect graphs. We develop a hypergraph characterization of F - G perfect graphs that leads to an alternate proof of previous results on Ki-perfect graphs as well as to a characterization of F - G perfect graphs for other instances of F and G.  相似文献   

12.
Let \mathbbK\mathbb{K} be a field, G a reductive algebraic \mathbbK\mathbb{K}-group, and G 1G a reductive subgroup. For G 1G, the corresponding groups of \mathbbK\mathbb{K}-points, we study the normalizer N = N G (G 1). In particular, for a standard embedding of the odd orthogonal group G 1 = SO(m, \mathbbK\mathbb{K}) in G = SL(m, \mathbbK\mathbb{K}) we have N ≅ G 1 ⋊ μ m ( \mathbbK\mathbb{K}), the semidirect product of G 1 by the group of m-th roots of unity in \mathbbK\mathbb{K}. The normalizers of the even orthogonal and symplectic subgroup of SL(2n, \mathbbK\mathbb{K}) were computed in [Širola B., Normalizers and self-normalizing subgroups, Glas. Mat. Ser. III (in press)], leaving the proof in the odd orthogonal case to be completed here. Also, for G = GL(m, \mathbbK\mathbb{K}) and G 1 = O(m, \mathbbK\mathbb{K}) we have N ≅ G 1 ⋊ \mathbbK\mathbb{K} ×. In both of these cases, N is a self-normalizing subgroup of G.  相似文献   

13.
It is known [M4] that K-orbits S and G-orbits S' on a complex flag manifold are in one-to-one correspondence by the condition that S ∩ S' is nonempty and compact. It is possible to replace K by some conjugate xKx−1 so that the correspondence is preserved. We investigate the sets C(S) of such x for various orbits S and their relations with each other. We prove that for classical groups the intersection C = ∩S C(S) equals D0Z where D0 = D0/K is the universal domain in G/K introduced in [AG] and Z is the center of G. As a corollary we prove that D0 is Stein for classical groups. Moreover we conjecture that C(S)0 = D0 for generic S where C(S)0 is the connected component of C(S) containing the identity.  相似文献   

14.
Let G be an abelian p-group and K be a field of the first kind with respect to p of char K ≠p and of sp(K) = N or NU {0}. Then it is shown that the normed Sylow p-subgroup S(KG) is torsion complete if and only if G is bounded (Theorem 1). An analogous fact is proved for the case when K is of the second kind (Theorem 2). These completely settle a conjecture posed by us in Compt. Rend. Acad. Bulg. Sci. (1993) and are also a supplement to our result in the modular case published in Acta Math. Hungar. (1997).  相似文献   

15.
Let G be a finite group andA be a normal subgroup ofG. We denote by ncc(A) the number ofG-conjugacy classes ofA andA is calledn-decomposable, if ncc(A)= n. SetK G = {ncc(A)|A ⊲ G}. LetX be a non-empty subset of positive integers. A groupG is calledX-decomposable, ifK G =X. Ashrafi and his co-authors [1-5] have characterized theX-decomposable non-perfect finite groups forX = {1, n} andn ≤ 10. In this paper, we continue this problem and investigate the structure ofX-decomposable non-perfect finite groups, forX = {1, 2, 3}. We prove that such a group is isomorphic to Z6, D8, Q8, S4, SmallGroup(20, 3), SmallGroup(24, 3), where SmallGroup(m, n) denotes the mth group of ordern in the small group library of GAP [11].  相似文献   

16.
Consider a finite group G. A subgroup is called S-quasinormal whenever it permutes with all Sylow subgroups of G. Denote by B sG the largest S-quasinormal subgroup of G lying in B. A subgroup B is called S-supplemented in G whenever there is a subgroup T with G = BT and BTB sG . A subgroup L of G is called a quaternionic subgroup whenever G has a section A/B isomorphic to the order 8 quaternion group such that LA and LB = 1. This article is devoted to proving the following theorem.  相似文献   

17.
In this paper we give a further investigation of the method introduced by the author in [1, Frequency-domain bounds for nonnegative unsharply band-limited functions] for proving bounds for functions with nonnegative Fourier transforms. We also dealt with the question of how large the supremum KS of all numbers |f(u)| is with f the Fourier transform of a nonnegative integrable function F and f(0) = 1, |f(ku)| ≤ ε for k ∈ S. Here u > 0 and S ⊂ {2, 3, . . .}. This problem was related in [1] to finding the infimum MS of all numbers Mh = maxϑ [(1−h(ϑ))/(1− cos ϑ)] over all 2π-periodic even, smooth functions h whose Fourier cosine coefficients ak vanish for k ∉ S, and it was proved and announced for several cases that MS (1−KS ) = 1. In this paper we prove the results announced in [1]. To that end we generalize the method given in [1] to include Fourier transforms f of probability measures on R and a certain generalized function h, and we show that the numbers KS, MS are assumed as |f(u)|, Mh for certain allowed f,h. Moreover, we establish a fundamental relation between finding the numbers KS, MS and the numbers KT, MT where T = {2, 3, . . .}\S. In particular, we show that MT = 2KS (2KS − 1)−1,KT = 1/2 MS(MS − 1)−1 and that MT (1 − KT) = 1,KSKT = 1/2 , whenever MS (1 − KS) = 1.  相似文献   

18.
Summary Given a knotKS 3, it is known a standard method for constructing a 4-coloured graph representing the closed orientable 3-manifoldM=M(K, d, ω) which is thed-fold covering space ofS 3 branched overK and associated to the transitived-representation ω of the knot group. In this paper we obtain a presentation of the fundamental group ofM, directly from the Wirtinger presentation of the knot group and from the transitived-representation ω.
Riassunto Dato un nodoKS 3, è noto un metodo standard per costruire un grafo 4-colorato rappresentante la 3-varietà chiusa ed orientabileM=M(K, d, ω) che è lo spazio di rivestimento diS 3 ramificato suK ed associato allad-rappresentazione transitiva ω del gruppo del nodo. In questo articolo si ottiene una presentazione del gruppo fondamentale diM, direttamente dalla presentazione di Wirtinger del gruppo del nodo e dallad-rappresentazione transitiva ω.


Work performed under the auspicies of the G.N.S.A.G.A. of the C.N.R. (National Research Council of Italy) and financially supported by M.P.I. (project ?Geometria delle Varietà differenziabili?).  相似文献   

19.
We introduce a new subgroup embedding property in a finite group called weakly S-quasinormality. We say a subgroup H of a finite group G is weakly S-quasinormal in G if there exists a normal subgroup K such that HKG and HK is S-quasinormally embedded in G. We use the new concept to investigate the properties of some finite groups. Some previously known results are generalized.  相似文献   

20.
A subgroup H of a finite group G is called a c*-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H ∩ K is an S-quasinormal embedded subgroup of G. In this paper, the structure of a finite group G with some c*-normal maximal subgroups of Sylow subgroups is characterized and some known related results are generalized.  相似文献   

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