关于CAP-子群的一点注记（英文）

对于有限群G的每一主因子H/K来说,若G的子群L满足LH=LK或者L∩H=L∩K,则称L是G的CAP-子群.本文通过假设G的每个非循环Sylow子群P有一个子群D使得1〈｜D｜〈｜P｜,且P的所有阶为｜D｜和2｜D｜（若P是非交换2-群且｜P∶D｜〉2）的子群H是G的CAP-子群,得到G为p-幂零群的一个结果.     

A Note on Diffeomorphism Groups of Closed Manifolds

In this short note, we construct a retracting deformation from group of orientation-preserving diffeomorphisms onto the group of volume-preserving diffeomorphismsof a compact smooth manifold. The retracting deformation isrealized by a moment map type of flow with the aid of the theory of quasi-linear parabolic equations.     

On quasi-isometric embeddings of Lamplighter groups

We denote by the Lamplighter group of a finite group . In this article, we show that if and are two finite groups with at least two elements, then there exists a quasi-isometric embedding from to . We also prove that the quasi-isometry group of contains all finite groups. We then show that the group of automorphisms of has infinite index in .

     

A Note on Property of Cauchy Integral on Classical Domains

In[1],ZhengXueanprovedthat:letRI(n×n)befirstclassicaldomain,Unbecharacteris-ticboundaryofRI,x∈Un,f(x)∈L2(Un).Asz=rx(0≤r<1)→x,Cauchyintegral∫Unf(y)det(I-zy′)-ndyconvergetoafunctioninL2(Un).Inthispaper,wewillfacusourselfonCauchyintegralofL2onclassicaldomains[2]andgetsomeproperties.Themainresultisfollowing:Theorem　LetRbeoneofclassicaldomains,LbecharacteristicboundaryofR,f∈L2(L),H(z,ξ)beCauchykernelofRandF(z)=∫Lf(u)H(z,u)u　z∈R,(1)wheretherightisLebesgueintegral;uist…     

A Note on Local Rigidity

The aim of this note is to give a geometric proof for classical local rigidity of lattices in semisimple Lie groups. We are reproving well known results in a more geometric (and hopefully clearer) way.     

本原Heronian三角形的一个注记

得到了无穷多个锐角本原Heronian三角形,其内切圆及三个旁切圆半径均为整数,并得到了无穷多个本原Heronian三角形,其内切圆及三个旁切圆半径均不为整数.     

Geometry of moduli space of sheaves on del Pezzo surfaces via Maruyama transform

In this paper, we prove that the moduli space of stable pairs (or sheaves) on del Pezzo surface S is isomorphic to the Maruyama type transformation of a projective bundle of a quiver representation space.     

Coarse homotopy groups

In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse homotopy groups. The main result is that the coarse homotopy groups of a cone over a compact simplicial complex coincide with the usual homotopy groups of the underlying compact simplicial complex. To prove this we develop geometric triangulation techniques for cones which we expect to be of relevance also in different contexts.     

A Note on Groups of Intermediate Growth

It was proved by Grigorchuk (1983 Grigorchuk , R. I. ( 1983 ). On the Milnor problem of group growth (Russian) . Dokl. Akad. Nauk SSSR 271 ( 1 ): 30 – 33 . English translation (1983). Soviet Math. Dokl. 28 ( 1 ): 23 – 26 . [Google Scholar]) that there exist groups which are neither of polynomial nor of exponential growth. Their growth is called “intermediate”. We show that every group of intermediate growth has either a residually finite quotient of intermediate growth or a simple section of intermediate growth.     

On orbit closures of spherical subgroups in flag varieties

Let be the flag variety of a complex semi-simple group G, let H be an algebraic subgroup of G acting on with finitely many orbits, and let V be an H-orbit closure in . Expanding the cohomology class of V in the basis of Schubert classes defines a union V₀ of Schubert varieties in with positive multiplicities. If G is simply-laced, we show that these multiplicities are equal to the same power of 2. For arbitrary G, we show that V₀ is connected in codimension 1. If moreover all multiplicities are 1, we show that the singularities of V are rational and we construct a flat degeneration of V to V₀ in . Thus, for any effective line bundle L on , the restriction map is surjective, and for all . Received: April 17, 2000     

3-幂零矩阵的Jordan标准型在GL_n(F)共轭作用下的迷向子群

研究迷向子群的结构是有限域上典型群几何中的一个重要问题.刻画了3-幂零矩阵的Jordan标准型在GLn(F)共轭作用下的迷向子群的结构.     

Classification of Fano manifolds containing a negative divisor isomorphic to projective space

We classify n-dimensional complex Fano manifolds X (n ≥ 3) containing a divisor E isomorphic to such that deg N _E/X is strictly negative. Our main tool is the extremal contraction theory together with numerical arguments on intersection numbers of divisors on X. In the last section, we consider, more generally, Fano manifolds X containing a prime divisor with Picard number one, and show that the Picard number of such X is less than or equal to three.      

The Invariant Fields of the Sylow Groups of Classical Groups in the Natural Characteristic

Let X be any finite classical group defined over a finite field of characteristic p > 0. In this article, we determine the fields of rational invariants for the Sylow p-subgroups of X, acting on the natural module. In particular, we prove that these fields are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant linear forms defining X.     

Remarks on Type III Unprojection

In this note we deal with rational curves in ? ³ which are images of a line by means of a finite sequence of cubo-cubic Cremona transformations. We prove that these curves can always be obtained applying to the line a sequence of such transformations increasing at each step the degree of the curve. As a corollary we get a result about curves that can give speciality for linear systems of ? ³.     

关于有限群不可约特征标零点的一点注记

在这篇文章中,我们分类了每一个非线性不可约特征标的零点集最多由$3$个共轭类组成的有限亚交换群的结构.     

A Note on Finitely A-Presented Abelian Groups

The class of mixed groups  was introduced by Glaz and Wickless. This article investigates subclasses  of  such that the functor Hom(A, ?)/t Hom(A, ?) between  and the category of right E(A)/tE(A)-modules is full.     

Quasi-isometric rigidity of nonuniform lattices in higher rank symmetric spaces

We compute the quasi-isometry group of an irreducible nonuniform lattice in a semisimple Lie group with finite center and no rank one factors, and show that any two such lattices are quasi-isometric if and only if they are commensurable up to conjugation.

     

关于Glauberman-Isaacs特征标对映的注记

假设群A经自同构互素地作用在G上.设χ是G的一个A-不变不可约特征标,π(G,A)表示Glauberman-Isaacs特征标对映.对于B≤A,T.R.Wolf曾猜想χπ(G,A)是χπ(G,B)a的一个不可约成份,此处C=CG(A).设G=N(X)H且(|N|,|H|)=1,假定H是A-不变的且N是一个Sylow塔群,N的Sylow-子群是交换的.在本文中,我们证明了如果这个猜想对所有H的A-不变子群成立,则猜想对G也成立.