真商群为s-自对偶群的有限p-群

如果有限群G的每个子群与G的某个商群同构,则称群G为s-自对偶群.如果s-自对偶群G的每个商群与G的某个子群同构,则称群G为自对偶群.本文分类了每个真商群均为s-自对偶群的有限p-群.作为推论,本文还分类了每个真截段均为s-自对偶群的有限p-群,每个真商群均为自对偶群的有限p-群,以及每个真截段均为自对偶群的有限p-群.     

换位子群为P 阶群的有限P- 群的自同构群(Ⅱ)

本文给出了换位子群为p 阶群的有限p-群的自同构群的结构定理的两点应用: 其一, 直接导出某些有限p-群的自同构群的结构; 其二, 对换位子群为p 阶群的有限p-群, 确定了其自同构群的阶何时达到最大值和最小值.     

极小非PNN-群

有限群G称作PNN-群,如果G的每一个极小子群X要么正规于G,要么是自正规化的.本文将讨论PNN-群的性质,并给出极小非PNN-群,也就是本身不是PNN-群,每个真子群都是PNN-群的有限群的完全分类.     

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.     

有限维线性空间上的极大线性变换群在几个线性空间上的群作用

群作用是研究群(特别是有限群)的一个外部方法.首先构作域上一有限维线性空间上的全线性变换半群的极大群,其次给出了三个群作用:极大群在其幺元的不动点子空间上的一个(自然的)群作用,两个极大群的(外)直积在两个极大群的幺元的不动点子空间的(外)直和上的一个群作用,两个极大群的(外)直积在两个极大群的幺元的不动点子空间之间的所有线性映射构成之集上的一个群作用.     

某些MI群

主要分类了亚循环的MI群及MA群,超特殊的MI群及MA群,并给出了一些一般的MI群和MA群的例子．     

无平方因子阶群的自同构群阶的上确界

群阶为素数方幂（即ｐ－ 群）时已得到该群自同构群阶的上确界,而对于其他情形的群,同样的问题要复杂得多． 本文在群阶无平方因子且为偶数时,给出了这类群的自同构群阶的上确界．     

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．     

置换性很好的一类群

主要研究子群置换性质对有限群结构的影响.通过子群的置换性得到一类群,即B 群.B群是全可置换群的扩展,利用全可置换群的p次中心扩张和子群的阶得到B群的一些性质并对B 群的结构进行一些刻画.应用B 群的结构得到有限p （p〉2）群为二元生成的B 群的充要条件.     

模糊群的公理体系

给出了模糊群的几个等价刻画,建立模糊群的公理体系并得到了五个最小完备系.此外还讨论以消去律为条件的模糊群的刻画,给出了有限模糊群和周期模糊群的最小完备系,同时也得到了一个一般模糊群的等价刻画,根据其三个推论可清楚地区分周期模糊群、无扭模糊群和混合模糊群.     

A CHARACTERIZATION OF LOCALLY COMPACT INNER AMENABLE GROUPS

For locally compact groups G, Kuan Yuan studied a notion of inner amenability groups, that is, if there exists an inner invariant mean on G. In this article, among other things, the author investigates the inner amenability on a locally compact group G. The author gives sufficient conditions and some necessary conditions about G to have an inner invariant mean.     

有限Abel群的一个特征

本文证明了有限群Ｇ是Ａｂｅｌ群当且仅当Ｇ_ｒ满足下列条件：（Ⅰ） Ｇ有一个幂自同构 ａ使得 ＣＧ（ａ）是一个初等 ＡｂｅｌＺ一群．（Ⅱ）Ｇ没有子群与２－群＜ａ,ｂ｜ａ~２~ｎ＝ｂ~２~ｍ＝１,ａ~ｂ＝ａ~（１＋２）~（ｎ－１）＞同构,其中ｎ≥３,ｎ≥ｍ．利用该结果,作者还证明若有限群Ｇ有一个幂自同构ａ使得Ｃ_Ｇ（ａ）是一个初等Ａｂｅｌ２－群,则Ｇ是幂零群     

On the Alexandrov problem of distance preserving mapping

In this paper the author has studied the Alexandrov problem of area preserving mappings in linear 2-normed spaces and has provided some remarks for the generalization of earlier results of H.Y. Chu, C.G. Park and W.G. Park.In addition the author has introduced the concept of linear (2,p)-normed spaces and for such spaces he has solved the Alexandrov problem.     

本原简单超图的指数集

设H是一个超图, 用H\+*和L(H)分别表示H的对偶超图和线图. 定义H的邻接图是由L(H\+*)和H的所有环组成的图, 记作G\-H. 若G\-H是本原的, 则称H是本原的, 并称γ(G\-H)为H的指数. 该文得到了所有n阶本原简单超图以及所有秩不小于3的n阶本原简单超图的指数集, 并分别刻划了其极超图.     

关于Thompson问题

1987年本文第二作者给J.G.Thompson教授的信中提出猜想:所有有限单群S,都能够用S的阶和S的元的阶的集合统一的刻画.在回信中,Thompson提出了他的关于有限群G可解性判断的问题.当G的素图非连通时,本文给出了J.G.Thompson问题的肯定回答.     

Boundedness of Multilinear Singular Integral Operators on Homogeneous Groups

Let G be a homogeneous group.In this paper,the author studies the boundedness of multi-sublinear operators on the product of weighted Lebesgue spaces on G.As its special case,the corresponding result of multilinear Calderón-Zygmund operators can be obtained.     

Average σ-K width of convolution function class ofL pq R inL q R

In this paper, we study the average n−K width of the convolution classB (G) (orB which the kernel G(x) is a PF density, in the metricR (orR and obtain some exact results. The author was supported by the National Natural Science Found of China.     

齐次群上多线性奇异积分算子的有界性

Let G be a homogeneous group.In this paper,the author studies the boundedness of multi-sublinear operators on the product of weighted Lebesgue spaces on G.As its special case,the corresponding result of multilinear Calderón-Zygmund operators can be obtained.     

FC groups whose periodic parts can be embedded in direct products of finite groups

In this note are considered FC groups whose periodic parts can be embedded in direct products of finite groups. It is shown that if the periodic part of an FC group G can be embedded in the direct product of its finite factor groups with respect to the normal subgroups of G whose intersection is the trivial subgroup, then G/Z (G) is a subgroup of a direct product of finite groups. It is also shown that if the periodic part of an FC group G is a group without a center, then G can be embedded in a direct product of finite groups without centers and a torsion-free Abelian group. Translated from Matematicheskie Zametki, Vol. 21, No. 1, pp. 9–20, January, 1977. The author is thankful to the referee for making many valuable remarks.     

Some Remarks on Singular Integrals and Power Weights on Vilenkin Groups

Let G be a Vilenkin group and T a sublinear operator. The author investigates under what weak conditions on the size of T, the Lp(G)-boundedness of T implies its Lp|x|α (G)-boundedness. For those sublinear operators which map Lp(G) to Lq(G) with p < q the author also obtains some similar results.