首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 31 毫秒
1.
If a topological group G acts on a topological space X, then we say that the action is orbit nonproper provided that, for some xX, the orbit map ggx:GX is nonproper. We consider the problem of classifying the connected, simply connected real Lie groups G admitting a locally faithful, orbit nonproper, isometric action on a connected Lorentz manifold. In an earlier paper, we found three collections of groups such that G admits such an action iff G is in one of the three collections. In another paper, we effectively described the first collection. In this paper, we show that the second collection contains a small, effectively described collection of groups, and, aside from those, it is contained in the union of the first and third collections. Finally, in a third paper, we effectively describe the third collection, thus solving the stated problem.  相似文献   

2.
Suppose we are given a group G\mit\Gamma and a tree X on which G\mit\Gamma acts. Let d be the distance in the tree. Then we are interested in the asymptotic behavior of the numbers ad: = # {w ? vertX : w=gv, g ? G , d(v0,w)=d }a_d:= \# \{w\in {\rm {vert}}X : w=\gamma {v}, \gamma \in {\mit\Gamma} , d({v}_0,w)=d \} if d? ¥d\rightarrow \infty , where v, vo are some fixed vertices in X.¶ In this paper we consider the case where G\mit\Gamma is a finitely generated group acting freely on a tree X. The growth function ?ad xd\textstyle\sum\limits a_d x^d is a rational function [3], which we describe explicitely. From this we get estimates for the radius of convergence of the series. For the cases where G\mit\Gamma is generated by one or two elements, we look a little bit closer at the denominator of this rational function. At the end we give one concrete example.  相似文献   

3.
If a topological group G acts on a topological space M, then we say that the action is orbit nonproper provided that, for some ,the orbit map is nonproper. In this paper we characterize the connected, simply connected Lie groups that admit a locally free, orbit nonproper action by isometries of a connected Lorentz manifold. We also consider a number of variants on this question. Submitted: November 1998, Revised version: April 1999, Final version: April 2000.  相似文献   

4.
We will say that a subgroup X of G satisfies property C in G if CG(X?Xg)\leqq X?Xg{\rm C}_{G}(X\cap X^{{g}})\leqq X\cap X^{{g}} for all g ? G{g}\in G. We obtain that if X is a nilpotent subgroup satisfying property C in G, then XF(G) is nilpotent. As consequence it follows that if N\triangleleft GN\triangleleft G is nilpotent and X is a nilpotent subgroup of G then CG(N?X)\leqq XC_G(N\cap X)\leqq X implies that NX is nilpotent.¶We investigate the relationship between the maximal nilpotent subgroups satisfying property C and the nilpotent injectors in a finite group.  相似文献   

5.
This paper is the second part of our investigations on doubly connected minimal surfaces which are stationary in a boundary configuration (G, S) (\Gamma, S) in \Bbb R 3 \Bbb R ^3 . The support surface S is a vertical cylinder above a simple closed polygon P(S) P(S) in the x,y-plane. The surrounding Jordan curve G \Gamma is chosen as a generalized graph above its convex projection curve P(G) P(\Gamma) . In [23] we have proved the existence of nonparametric minimal surfaces X of annulus type spanning such boundary configurations. We study the behaviour of these minimal surfaces at the edges of the support surface S. In particular we discuss the phenomenon of edge-creeping, i. e. the fact that the free trace of X may attach to an edge of S in a full interval. We prove that a solution X cuts any intruding edge of S perpendicularly. On the other hand, we derive a condition which forces X to exhibit the edge-creeping behaviour. Depending on the symmetries of (G, S) (\Gamma, S) we give bounds on the number of edges where edge-creeping occurs. Let (x,y,Z (x,y)) (x,y,\hbox {Z} (x,y)) for (x,y) ? G (x,y)\in G be the nonparametric representation of X. Then at every vertex Q of P(S) P(S) the radial limits of Z from all directions in G exist.  相似文献   

6.
In this note we prove that every infinite group G is 3-abelian (i.e. (ab)3 = a3b3 for all a, b in G) if and only if in every two infinite subsets X and Y of G there exist x ? Xx\in X and y ? Yy\in Y such that (xy)3 = x3y3.  相似文献   

7.
Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module. If G/HP(V) is a spherical orbit and if X = [`(G/H)] X = \overline {G/H} is its closure, then we describe the orbits of X and those of its normalization [(X)\tilde] \tilde{X} . If, moreover, the wonderful completion of G/H is strict, then we give necessary and sufficient combinatorial conditions so that the normalization morphism [(X)\tilde] ? X \tilde{X} \to X is a homeomorphism. Such conditions are trivially fulfilled if G is simply laced or if H is a symmetric subgroup.  相似文献   

8.
9.
Let n be an integer and Bn \mathcal B_n be the variety defined by the law [xn,y][x,yn]-1 = 1.¶ Let Bn* \mathcal B_n^* be the class of groups in which for any infinite subsets X, Y there exist x ? X x \in X and y ? Y y \in Y such that [xn,y][x,yn]-1 = 1. For $ n \in {\pm 2, 3\} $ n \in {\pm 2, 3\} we prove that¶ Bn* = Bn èF \mathcal B_n^* = \mathcal B_n \cup \mathcal F , F \mathcal F being the class of finite groups. Also for $ n \in {- 3, 4\} $ n \in {- 3, 4\} and an infinite group G which has finitely many elements of order 2 or 3 we prove that G ? Bn* G \in \mathcal B_n^* if and only if G ? Bn G \in \mathcal B_n .  相似文献   

10.
Summary. Let \Bbb K {\Bbb K} be either the field of reals or the field of complex numbers, X be an F-space (i.e. a Fréchet space) over \Bbb K {\Bbb K} n be a positive integer, and f : X ? \Bbb K f : X \to {\Bbb K} be a solution of the functional equation¶¶f(x + f(x)n y) = f(x) f(y) f(x + f(x)^n y) = f(x) f(y) .¶We prove that, if there is a real positive a such that the set { x ? X : |f(x)| ? (0, a)} \{ x \in X : |f(x)| \in (0, a)\} contains a subset of second category and with the Baire property, then f is continuous or { x ? X : |f(x)| ? (0, a)} \{ x \in X : |f(x)| \in (0, a)\} for every x ? X x \in X . As a consequence of this we obtain the following fact: Every Baire measurable solution f : X ? \Bbb K f : X \to {\Bbb K} of the equation is continuous or equal zero almost everywhere (i.e., there is a first category set A ì X A \subset X with f(X \A) = { 0 }) f(X \backslash A) = \{ 0 \}) .  相似文献   

11.
Let X be a smooth algebraic surface, L ? Pic(X) L \in \textrm{Pic}(X) and H an ample divisor on X. Set MX,H(2; L, c2) the moduli space of rank 2, H-stable vector bundles F on X with det(F) = L and c2(F) = c2. In this paper, we show that the geometry of X and of MX,H(2; L, c2) are closely related. More precisely, we prove that for any ample divisor H on X and any L ? Pic(X) L \in \textrm{Pic}(X) , there exists n0 ? \mathbbZ n_0 \in \mathbb{Z} such that for all n0 \leqq c2 ? \mathbbZ n_0 \leqq c_2 \in \mathbb{Z} , MX,H(2; L, c2) is rational if and only if X is rational.  相似文献   

12.
Let G be a reductive algebraic group defined over \Bbb Q {\Bbb Q} . Let P, P' be parabolic subgroups of G, defined over \Bbb Q {\Bbb Q} , and let _boxclose_boxclose, a_P') t \in W({\frak a}_{P}, {\frak a}_{P'}) . In this paper we study the intertwining operator MP¢|P(t,l), l ? \frak a*P,\Bbb C M_{P' \vert P}(t,\lambda),\,\lambda \in {\frak a}^*_{P,{\Bbb C}} , acting in corresponding spaces of automorphic forms. One of the main results states that each matrix coefficient of MP¢|P(t,l) M_{P' \vert P}(t,\lambda) is a meromorphic function of order £ n + 1 \le n + 1 , where n = dim G. Using this result, we further investigate the rank one intertwining operators, in particular, we study the distribution of their poles.  相似文献   

13.
Given a binary relation R between the elements of two sets X and Y and a natural number k, it is shown that there exist k injective maps f1, f2,...,fk: X \hookrightarrow Y X \hookrightarrow Y with # {f1(x), f2(x),...,fk(x)}=k    and    (x,f1(x)), (x, f2(x)),...,(x, fk(x)) ? R \# \{f_1(x), f_2(x),...,f_k(x)\}=k \quad{\rm and}\quad (x,f_1(x)), (x, f_2(x)),...,(x, f_k(x)) \in R for all x ? X x \in X if and only if the inequality k ·# A £ ?y ? Y min(k, #{a ? A | (a,y) ? R}) k \cdot \# A \leq \sum_{y \in Y} min(k, \#\{a \in A \mid (a,y) \in R\}) holds for every finite subset A of X, provided {y ? Y | (x,y) ? R} \{y \in Y \mid (x,y) \in R\} is finite for all x ? X x \in X .¶Clearly, as suggested by this paper's title, this implies that, in the context of the celebrated Marriage Theorem, the elements x in X can (simultaneously) marry, get divorced, and remarry again a partner from their favourite list as recorded by R, for altogether k times whenever (a) the list of favoured partners is finite for every x ? X x \in X and (b) the above inequalities all hold.¶In the course of the argument, a straightforward common generalization of Bernstein's Theorem and the Marriage Theorem will also be presented while applications regarding (i) bases in infinite dimensional vector spaces and (ii) incidence relations in finite geometry (inspired by Conway's double sum proof of the de Bruijn-Erdös Theorem) will conclude the paper.  相似文献   

14.
Let a linear algebraic group G act on an algebraic variety X. Classification of all these actions, in particular birational classification, is of great interest. A complete classification related to Galois cohomologies of the group G was established. Another important question is reducibility, in some sense, of this action to an action of G on an affine variety. It has been shown that if the stabilizer of a typical point under the action of a reductive group G on a variety X is reductive, then X is birationally isomorphic to an affine variety [`(X)] \bar X with stable action of G. In this paper, I show that if a typical orbit of the action of G is quasiaffine, then the variety X is birationally isomorphic to an affine variety [`(X)] \bar X .  相似文献   

15.
Let A ì BA\subset B be rings. We say that A is t-closed in B, if for each a ? Aa\in A and b ? Bb\in B such that b2-ab,b3-ab2 ? Ab^2-ab,b^3-ab^2\in A, then b ? Ab\in A. We present a sufficient condition for the ring A[[X1,?,Xn]]A[[X_1,\ldots ,X_n]] to be t-closed in B[[X1,?,Xn]]B[[X_1,\ldots ,X_n]]. By an example, we show that our condition is not necessary. Even though the question is still open, some important cases are treated. For example, if A ì BA\subset B is an integral extension, or if A is p-injective, then A[[X1,?,Xn]]A[[X_1,\ldots ,X_n]] is t-closed in B[[X1,?,Xn]]B[[X_1,\ldots ,X_n]] if and only if A is t-closed in B.  相似文献   

16.
A polynomial P(X) with coefficients {ǃ} of odd degree N - 1 is cyclotomic if and only if¶¶P(X) = ±Fp1X)Fp2Xp1) ?FprXp1 p2 ?pr-1) P(X) = \pm \Phi_{p1} (\pm X)\Phi_{p2}(\pm X^{p1}) \cdots \Phi_{p_r}(\pm X^{p1 p2 \cdots p_r-1}) ¶where N = p1 p2 · · · pr and the pi are primes, not necessarily distinct, and where Fp(X) : = (Xp - 1) / (X - 1) \Phi_{p}(X) := (X^{p} - 1) / (X - 1) is the p-th cyclotomic polynomial. This is a conjecture of Borwein and Choi [1]. We prove this conjecture for a class of polynomials of degree N - 1 = 2r pl - 1 N - 1 = 2^{r} p^{\ell} - 1 for any odd prime p and for integers r, l\geqq 1 r, \ell \geqq 1 .  相似文献   

17.
Let R be a right near-ring with identity and Mn(R) be the near-ring of n 2 n matrices over R in the sense of Meldrum and Van der Walt. In this paper, Mn(R) is said to be s\sigma-generated if every n 2 n matrix A over R can be expressed as a sum of elements of Xn(R), where Xn(R)={fijr | 1\leqq i, j\leqq n, r ? R}X_n(R)=\{f_{ij}^r\,|\,1\leqq i, j\leqq n, r\in R\}, is the generating set of Mn(R). We say that R is s\sigma-generated if Mn(R) is s\sigma-generated for every natural number n. The class of s\sigma-generated near-rings contains distributively generated and abstract affine near-rings. It is shown that this class admits homomorphic images. For abelian near-rings R, we prove that the zerosymmetric part of R is a ring, so the class of zerosymmetric abelian s\sigma-generated near-rings coincides with the class of rings. Further, for every n, there is a bijection between the two-sided subgroups of R and those of Mn(R).  相似文献   

18.
Suppose G is a transitive permutation group on a finite set W\mit\Omega of n points and let p be a prime divisor of |G||G|. The smallest number of points moved by a non-identity p-element is called the minimal p-degree of G and is denoted mp (G). ¶ In the article the minimal p-degrees of various 2-transitive permutation groups are calculated. Using the classification of finite 2-transitive permutation groups these results yield the main theorem, that mp(G) 3 [(p-1)/(p+1)] ·|W|m_{p}(G) \geq {{p-1} \over {p+1}} \cdot |\mit\Omega | holds, if Alt(W) \nleqq G {\rm Alt}(\mit\Omega ) \nleqq G .¶Also all groups G (and prime divisors p of |G||G|) for which mp(G) £ [(p-1)/(p)] ·|W|m_{p}(G)\le {{p-1}\over{p}} \cdot |\mit\Omega | are identified.  相似文献   

19.
Soient G un groupe de Lie semi-simple, réel, connexe et de centre fini, \mathfrak a \mathfrak a un sous-espace de Cartan de l‘algèbre de Lie de G et \mathfrak a+ ì \mathfrak a \mathfrak a^{+} \subset \mathfrak a une chambre de Weyl fermée de \mathfrak a \mathfrak a . Si G \Gamma est un sous-groupe discret Zariski dense de G, nous lui associons une fonction homogène yG : \mathfrak a+ ? \mathbb R è{-¥} \psi_{\Gamma} : \mathfrak a^{+} \rightarrow \mathbb {R} \cup \{-\infty\} qui généralise l‘exposant de convergence de G \Gamma considéré en \mathbb R \mathbb {R} -rang 1. Nous montrons alors que cette fonction est concave. Dans un travail ultérieur, nous en déduirons des constructions de généralisations des mesures de Patterson-Sullivan.¶ Nous démontrons aussi des analogues de nos résultats sur les corps locaux.  相似文献   

20.
Summary. We investigate cellular automata (CA) with a local rule f: G2 ? G \phi : G^2 \rightarrow G , where the local rule defines a quasigroup structure (Latin square) on the finite set G. If the quasigroup is semisymmetric or totally symmetric, some top-down equilateral triangular subsets of the CA-orbits, the so-called \triangledown \triangledown -configurations, exhibit certain symmetries. The most interesting symmetries are the rotational and the total (dihedral) symmetries, which may be considered in conjunction with certain automorphisms.¶We first explore the conditions for quasigroups to be symmetric (or for local CA-rules to allow symmetric \triangledown \triangledown -configurations), and how to construct symmetric quasigroups by prolongation, i.e., by steadily increasing the order of the quasigroup, thereby conserving the symmetry. Then we study rotationally or totally symmetric \triangledown \triangledown -configurations. We begin with the existence of symmetric \triangledown \triangledown -configurations of arbitrary size N and N o 0,1 mod 3 N \equiv 0,1\,{\rm mod}\,3 , and show that symmetric \triangledown \triangledown -configurations of size N o 2 mod 3 N \equiv 2\,{\rm mod}\,3 exist under mild conditions on J. We present explicit formulas for the number of distinct symmetric \triangledown \triangledown -configurations. By studying the combined group action of the dihedral (or rotational) group and the automorphism group of the quasigroup G on the \triangledown \triangledown -configurations of size N, we are able to classify and count the number of different equivalence classes of \triangledown \triangledown -configurations.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号