n-极大子群为共轭可换的有限群

群G的子群H称为G的共轭可换子群,若HHg=HgH,对任意g∈G都成立,本文考查了n-极大子群为共轭可换时对有限群构造的影响.     

On the Normal Subgroup with Exactly Two G-Conjugacy Class Sizes

Let G be a finite group with a non-central Sylow r-subgroup R, Z（G） the center of G, and N a normal subgroup of G. The purpose of this paper is to determine the structure of N under the hypotheses that N contains R and the G-conjugacy class size of every element of N is either i or m. Particularly, it is shown that N is Abelian if N ∩ Z（G）=1 and the G-conjugacy class size of every element of N is either 1 or m.     

The probability that <Emphasis Type="Italic">r</Emphasis> elements of a rank <Emphasis Type="Italic">n</Emphasis> free group generate a rank <Emphasis Type="Italic">r</Emphasis> subgroup

Granted the three integers n ≥ 2, r, and R, consider all ordered tuples of r elements of length at most R in the free group F _n . Calculate the number of those tuples that generate in F _n a rank r subgroup and divide it by the number of all tuples under study. As R → ∞, the limit of the ratio is known to exist and equal 1 (see [1]). We give a simple proof of this result.     

Quotients of subdirect products of groups

We find the sharp bound for the nilpotency class of the quotients of subdirect products of groups.     

单向双筋板结构件共振疲劳试验及分析

航空航天领域广泛存在着振动疲劳问题,严重危及飞行器结构的安全可靠性。本文首先设计了激振器直接作用于试件的力激励振动疲劳试验系统,并提出了跟踪结构共振频率的频带激励共振疲劳寿命测试方法;而后利用试件进行了频带激励下的定应变共振或定载荷共振结构振动疲劳试验;最后针对试验结果分析与讨论了可能影响结构振动疲劳寿命的各种因素。结论表明,试验结构件的边界条件、初始条件以及结构动力学特性等都可能是影响振动疲劳寿命的关键因素。频带激励共振疲劳试验方法为振动疲劳寿命曲线的测试积累了经验。     

Finite groups with some pronormal subgroups

A subgroup H of finite group G is called pronormal in G if for every element x of G, H is conjugate to H ^x in 〈H, H ^x 〉. A finite group G is called PRN-group if every cyclic subgroup of G of prime order or order 4 is pronormal in G. In this paper, we find all PRN-groups and classify minimal non-PRN-groups (non-PRN-group all of whose proper subgroups are PRN-groups). At the end of the paper, we also classify the finite group G, all of whose second maximal subgroups are PRN-groups.     

典型荷载条件下淤泥孔径分布特征核磁共振试验研究

模拟了淤泥地基加固工况对应的几种典型荷载效应,并利用核磁共振测试寻求典型荷载水平和速率下,淤泥孔隙及其孔径分布的变化规律,以探讨淤泥地基典型加固条件下微细观结构的三维响应.结果表明:在一定压力作用下,淤泥中最大孔隙数将会减少,应力水平越高,减少量越大,而当冲击荷载达到更高的某一水平时,淤泥中最大孔隙和最小孔隙所占比例均会减小,孔隙更趋于均匀;约束样品的侧限刚度将会增加淤泥土的总受力水平,进而更易减小大孔隙所占比例;当荷载水平680 kPa时,加载速率是决定相对最大孔隙占总孔隙数比例的关键因素,速率较小会使得该比例增大,速率较大则使得该比例减小,其界限值在0.8 MPa/s与1.6 MPa/s之间;一定的冲击荷载和速率水平下,随着作用次数即总能量的提高,淤泥中的相对大孔隙和最大孔隙部分会明显减少,而当间隔时间较短的作用次数再提高时,上述效应会降低;对于有效减少较大孔隙而言,淤泥受冲击的次数存在某个合适的量值.上述规律有助于从内部本质上寻求和掌握各种静动力排水固结法处理淤泥类软基的微观机理,为其科学设计及施工优化提供了进一步的依据.     

极大子群的性质对有限群结构的影响

设H为有限群G的一个子群。称H在G中是s-半正规的,若对任意的素数p||G|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G);称H在G中是c-可补的,若存在G的子群N,使得G=HN且H∩N≤HG=CoreG(H)。证明了下面定理设F是一个包含超可解群类U的饱和群系,H△G,且G/H∈F。则G∈F,若下列条件之一成     

Classification of torsion-free genus zero congruence groups

We study and classify all torsion-free genus zero congruence subgroups of the modular group.

     

Rank Tests Based on Exceeding Observations

Rank tests based on the maximum number of exceeding observations for several standard nonparametric hypotheses are proposed. An approach to constructing nonparametric rank tests via metrics on the permutation group is used. The test statistics are based on a metric induced by Chebyshev's norm.