关于有限群的特征标次数的商

设Ｇ是有限非Ａｂｅｌ群，Ｉｒｒ（Ｇ）是Ｇ的一切不可约特征标组成的集合。在这篇文章中，我们考虑商集，考察对这些数作的某些假设如何影响Ｇ的结构。例如，设是ｎ的素数分解式。置及．我们证明：如果Ｇ是非可解的且Ｗ（Ｇ）＝４，则Ｇ恰是下述群之一：Ｚ＿ｐ×Ａ＿５，ＳＬ（２，５），Ｓ＿５，ＰＳＬ（２，７），ＰＳＬ（２，１１）和ＰＳＬ（２，１３）。     

外FO-群

如果群G的所有真商群都是FO-群,但是群G本身不是FO-群,则称G为外FO-群,本文将给出外FO-群完全的结构描述.     

外FO-群

如果群 G 的所有真商群都是 FO-群,但是群 G 本身不是 FO-群,则称 G 为外 FO-群,本文将给出外 FO-群完全的结构描述．     

Profinite Groups Admitting Just Infinite Quotients

 A profinite group is said to be just infinite if each of its proper quotients is finite. We address the question which profinite groups admit just infinite quotients. It is proved that any profinite group whose order (as a supernatural number) is divisible only by finitely many primes admits just infinite quotients. It is shown that if a profinite group G possesses the property in question then so does every open subgroup and every finite extension of G. Received 20 July 2001     

Groups Acting on Protrees

A group is accessible if there is a G-tree T such that everyedge stabilizer is finite and every vertex stabilizer has atmost one end. A group is inaccessible if it is not accessible.In [6] I began the study of group actions on protrees. Theseactions arise naturally when considering inaccessible groups.This study is continued in this paper.     

Base Sizes and Regular Orbits for Coprime Affine Permutation Groups

Let G be a permutation group on a finite set . A sequence B=(₁,..., _b) of points in is called a base if its pointwise stabilizerin G is the identity. Bases are of fundamental importance incomputational algorithms for permutation groups. For both practicaland theoretical reasons, one is interested in the minimal basesize for (G, ), For a nonredundant base B, the elementary inequality2^|B||G|||^|B| holds; in particular, |B|log|G|/log||. In the casewhen G is primitive on , Pyber [8, p. 207] has conjectured thatthe minimal base size is less than Clog|G|/log|| for some (large)universal constant C. It appears that the hardest case of Pyber's conjecture is thatof primitive affine groups. Let H=GV be a primitive affine group;here the point stabilizer G acts faithfully and irreduciblyon the elementary abelian regular normal subgroup V of H, andwe may assume that =V. For positive integers m, let mV denotethe direct sum of m copies of V. If (v₁, ..., v_m)mV belongsto a regular G-orbit, then (0, v₁, ..., v_m) is a base for theprimitive affine group H. Conversely, a base (₁, ..., _b) forH which contains 0V= gives rise to a regular G-orbit on (b–1)V. Thus Pyber's conjecture for affine groups can be viewed asa regular orbit problem for G-modules, and it is therefore aspecial case of an important problem in group representationtheory. For a related result on regular orbits for quasisimplegroups, see [4, Theorem 6].     

其真商群是周期FC-群的群

利用外FC-群的结果,给出了其真商群为周期FC-群但它本身不具备这种性质的群的结构的满意描述.     

Augmentation Quotients for Complex Representation Rings of Generalized Quaternion Groups

Denote by Q_m the generalized quaternion group of order 4m. Let R(Q_m) be its complex representation ring, and Δ(Q_m) its augmentation ideal. In this paper, the author gives an explicit Z-basis for the Δ~n(Q_m) and determines the isomorphism class of the n-th augmentation quotientΔ~n(Q_m)/(Δ~(n+1)(Q_m))for each positive integer n.     

Strong Embeddability for Groups Acting on Metric Spaces

The strong embeddability is a notion of metric geometry, which is an intermediate property lying between coarse embeddability and property A. In this paper, the permanence properties of strong embeddability for groups acting on metric spaces are studied. The authors show that a finitely generated group acting on a finitely asymptotic dimension metric space by isometries whose $K$-stabilizers are strongly embeddable is strongly embeddable. Moreover, they prove that the fundamental group of a graph of groups with strongly embeddable vertex groups is also strongly embeddable.     

Entropy and Arithmetic Quotients for Simple Automorphism Groups of Geometric Manifolds

Let G be a connected simple Lie group, and suppose G acts on a compact real analytic manifold M. Assume that G preserves a unimodular rigid geometric structure, for example a connection and a volume form. The aim of this paper is to describe the measure theoretic structure of such actions, when -rank(G)2.     

Differential Forms and Smoothness of Quotients by Reductive Groups

Let :XY be a good quotient of a smooth variety X by a reductive algebraic group G and 1k dim (Y) an integer. We prove that if, locally, any invariant horizontal differential k-form on X (resp. any regular differential k-form on Y) is a Kähler differential form on Y then codim(Y _sing)>k+1. We also prove that the dualizing sheaf on Y is the sheaf of invariant horizontal dim(Y)-forms.     

Three-Dimensional Classical Groups Acting on Polytopes

Let V be a three-dimensional vector space over a finite field. We show that any irreducible subgroup of GL(V) that arises as the automorphism group of an abstract regular polytope preserves a nondegenerate symmetric bilinear form on V. In particular, the only classical groups on V that arise as automorphisms of such polytopes are the orthogonal groups.     

一类p~3阶群的Burnside环之增广商群

群环理论将群论和环论有机地结合了起来,是代数学中的重要分支之一,其中增广理想和增广商群是群环理论中的一个经典课题.设G有限群,分别记的Burnside环及其增广理想为Ω(G)和Δ(G).本文对任意正整数n,具体构造了Δ~n(I_p)作为自由交换群的一组基,并确定了商群Δ~n(I_p)/Δ~(n+1)(I_p)的结构,其中I_p=〈a,b|a~(p~2)=b~p=1,b~(-1)ab=a~(p+1)〉,p为奇素数.     

一类p4阶群的Burnside环之增广商群

设G是有限群,以 Ω(G)和 Δ(G)分别表示G的Burside环及其增广理想.对任意的自然数n,具体构造了 Δn(Ip)作为自由(Z)-模的一组基底,并给出了商群 Δn(Ip)/Δn+1(Ip)的结构,其中IP=,p是奇素数.     

最大Abel商群为局部循环群的可解群

从自同构群的角度出发,给出了一些具有有限性条件的、最大Abel商群为局部循环群的可解群的结构．