互素作用下的不变块(英文)

令A,G为有限群且(|A|,|G|)=1.设A通过自同构作用在G上.令B是G的A-不变块.若B的每一个指标都是A-不变的,且B的亏群是循环群,则A中心化B的某一亏群.     

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.     

有限Hopf C~*-代数的表示与对偶

设A是有限维Hopf C-代数,H是Hilbert空间.如果存在A在L(H)上的作用γ,在此作用下,L(H)成为具有共轭性质的模代数且H上内积是A-不变的,则A存在惟一的C-表示(θ,H),L(H)的A-不变子空间恰好是θ(A)的换位子.     

Abel群的一些分解定理的推广(Ⅱ)

本文讨论了2类具体的主理想整环上的拟循环模,研究了A-宽有限的向量空间,刻画了该类向量空间的结构,阐述了A-宽有限的向量空间的A-不变子空间构成的偏序集必满足极小条件,并给出了带有线性变换的向量空间作为F[λ]-模构成拟循环模的一个充要条件.     

On the structure of a mutually permutable product of finite groups

Let a finite group \({G = AB}\) be the product of the mutually permutable subgroups A and B. We investigate the structure of G given by conditions on conjugacy class sizes of elements in \({A \cup B}\) . Some recent results are extended.     

恰有两个子群共轭类长的有限群

设G是有限群,Ns(G)表示G的子群共轭类长构成的集合.本文研究Ns(G)中只有两个元素时有限群G的结构,在非幂零情形时给出了G的完全分类,在幂零情形时获得了G的一些性质.     

Characterization of three types of planar spaces with invisible planes

In this paper we characterize a class of finite planar spaces whose planes have two sizes.Dedicato alla memoria dell'amico e Maestro Giuseppe TalliniWork supported by G.N.S.A.G.A. of C.N.R. and the projects M.U.R.S.T. 40 %     

The Divisibility Graph for F-Groups

Mathematical Notes - A graph $$D(G)$$ is called the divisibility graph of $$G$$ if its vertex set is the set of noncentral conjugacy class sizes of $$G$$ and there is an edge between vertices $$a$$...     

A result analogous to G. Szego’s theorem

The paper proves a new result similar to the well known theorems of G. Szego and A. Kolmogorov on the best approximation by analytic polynomials in weighted L ^p spaces. Such results are essential in prediction theory for stationary processes. It is well known, that for one step prediction, the size of the best approximation is the same for all p. The paper proves that for two step prediction the best approximation sizes are different for p = 2 and p = ∞.     

A groupoid generalisation of Leavitt path algebras

Let \(G\) be a locally compact, Hausdorff, étale groupoid whose unit space is totally disconnected. We show that the collection \(A(G)\) of locally-constant, compactly supported complex-valued functions on \(G\) is a dense \(*\) -subalgebra of \(C_c(G)\) and that it is universal for algebraic representations of the collection of compact open bisections of \(G\) . We also show that if \(G\) is the groupoid associated to a row-finite graph or \(k\) -graph with no sources, then \(A(G)\) is isomorphic to the associated Leavitt path algebra or Kumjian–Pask algebra. We prove versions of the Cuntz–Krieger and graded uniqueness theorems for \(A(G)\) .     

Multiplying a conjugacy class by its inverse in a finite group

Suppose that G is a finite group and K is a non-trivial conjugacy class of G such that KK^?1 = 1 ∪ D ∪ D^?1 with D a conjugacy class of G. We prove that G is not a non-abelian simple group and we give arithmetical conditions on the class sizes determining the solvability and the structure of 〈K〉 and 〈D〉.     

Gorenstein范畴上的一个问题

设■是阿贝尔范畴,■是■的子范畴.Sather-Wagstaff, Sharif和White引入了Gorenstein子范畴的概念,记为■.我们用■(相应地,■)代表纯投射R-模类(相应地,投射R-模类).本文给出了一类满足条件"■"的环,由此给出了当■是■的子范畴时,■是否包含在■中的一个否定回答.进一步,刻画了包含关系■和■何时成立.     

Simplicity of normal subgroups and conjugacy class sizes

Given a finite group \(G\) which possesses a non-abelian simple normal subgroup \(N\) having exactly four \(G\) -class sizes, we prove that \(N\) is isomorphic to PSL \((2, 2^a)\) with \(a\ge 2\) . Thus, we obtain an extension for normal subgroups of the classic N. Itô’s theorem which characterizes those finite simple groups with exactly four class sizes.     

Certain Cuntz Semigroup Properties of Certain Crossed Product C*-algebras

We show that the following properties of the C^*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an application,let A be an infinite dimensional simple unital C-algebra such that A has one of the above-listed properties.Suppose that α:G→Aut(A) is an action of a finite group G on A which has the tracial Rokhlin property.Then the crossed product C^*-algebra C^*(G,A,α) also has the property under consideration.     

Non-abelian tensor square of finite-by-nilpotent groups

Let G be a group. We denote by \({\nu(G)}\) an extension of the non-abelian tensor square \({G \otimes G}\) by \({G \times G}\). We prove that if G is finite-by-nilpotent, then the non-abelian tensor square \({G \otimes G}\) is finite-by-nilpotent. Moreover, \({\nu(G)}\) is nilpotent-by-finite (Theorem A). Also we characterize BFC-groups in terms of \({\nu(G)}\) among the groups G in which the derived subgroup is finitely generated (Theorem B).     

Possible cardinalities of irredundant bases for finite closure structures

We indicate certain connections between the rank and cardinality of a finite closure structure, and the relative sizes of its irredundant bases. A class of examples is described which shows that in general our theorem can not be strengthened.     

On the conjugate type vector and the structure of a normal subgroup

Czechoslovak Mathematical Journal - Let N be a normal subgroup of a group G. The structure of N is given when the G-conjugacy class sizes of N is a set of a special kind. In fact, we give the...     

Handling load with less stress

We study how the average performance of a system degrades as the load nears its peak capacity. We restrict our attention to the performance measures of average sojourn time and the large deviation rates of buffer overflow probabilities. We first show that for certain queueing systems, the average sojourn time of requests depends much more weakly on the load ρ than the commonly observed 1/(1−ρ) dependence for most queueing policies. For example, we show that for an M/G/1 system under the preemptive Shortest Job First (pSJF) policy, the average sojourn time varies as log (1/(1−ρ)) with load for a certain class of distributions. We observe that such results hold even for more restricted policies. We give some examples of non-preemptive policies and policies that do not use the knowledge of job sizes while scheduling, where the dependence of average sojourn time on load is significantly better than 1/(1−ρ). Similar results hold even for very simple non-preemptive threshold based policies that partition all the jobs into two job classes based on a fixed threshold and do FIFO within each class. Finally we study the large deviations rate of the queue length under a simple dedicated partition-based policy.     

Infinite locally dihedral groups as automorphism groups

If \(A\) is a nontrivial torsion-free, locally cyclic group with no nontrivial divisible quotients, and \(G\) is the split extension of \(A\) by a group of order 2 acting on \(A\) by means of the inverting map, then \(G\simeq {{{\mathrm{Aut}}}G} \). We prove that in no other case the full automorphism group of a group is infinite and locally dihedral.     

Graph clustering with a constraint on cluster sizes

A graph clustering problem is under study (also known as the graph approximation problem) with a constraint on cluster sizes. Some new approximation algorithm is presented for this problem, and performance guarantee of the algorithm is obtained. It is shown that the problem belongs to the class APX for every fixed p, where p is the upper bound on the cluster sizes.