群的根性的一般理论

该文列举了任意群的根性的定义,并给出了任意群的根性的几个例子,同时还研究了群的根性的性质.     

直觉模糊群的子直觉模糊群和正规子直觉模糊群

设G为直觉模糊二元运算下的直觉模糊群,给出了G子直觉模糊群和正规子直觉模糊群的定义,讨论并证明了子直觉模糊群和正规子直觉模糊群的一些性质。     

基于模糊二元运算的直觉模糊群

为了使直觉模糊群也具有经典的结构,首先给出经典集合G的一种直觉模糊二元运算,利用这种直觉模糊二元运算定义了直觉模糊群,讨论这种直觉模糊群的一些性质,并给出直觉模糊群的两种等价定义。由于直觉模糊群具有和群一样经典的结构,因此,使直觉模糊代数的深入研究有了充分的理论基础。     

L-fuzzy群范畴中的乘积运算

文献[1]提出了Fuzzy群的概念,[2]讨论了Fuzzy群组成的范畴,本文在文献[1-6]的基础上,引入LF群范畴的概念,该范畴以Fuzzy群范畴作为子范畴,证明了LF群范畴对乘积运算封闭,同时给出了LF群范畴中的乘积的具体结构和一些性质。     

论有限群元素共轭类的平均长度

本文研究有限群元素共轭类的平均长度问题.利用初等群论方法和有限群特征标理论,在共轭类平均长度为某一定数时,获得了对有限群结构的刻划,且对有限群数量性质的研究是有意义的.     

L—Fuzzy群的同志和同构

本文研究了Ｌ—Ｆｕｚｚｙ群的同态和同构，给出了它们的一些性质，并把群论中的同态定理和同构定理推广到Ｌ—Ｆｕｚｚｙ群上     

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.     

基于模糊二元运算的模糊群的若干性质

给出一种新的模糊二元运算,利用这种运算导出集合G中元素间的一种运算(仍称之为模糊二元运算),然后给出新模糊群的定义.讨论了这种基于模糊二元运算的模糊群的一系列的概念以及性质.     

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.     

某类群的增广理想的基底及其商群的结构

本文研究了一类具有完全正规子群的有限群之增广理想及增广商群结构的问题.利用完全群的一些性质及数学归纳法,得到了此类群任意次增广理想的一组基底,并且解决了增广商群的结构问题.     

Hereditary Upper Radical Properties and Dual Supplementing Radicals of Hereditary Radicals of Groups

One aim of this paper is to prove that for any hereditary radical property 𝒫, there exists a radical property 𝒫′ supplementing 𝒫. Certain hereditary upper radical properties of groups are constructed, and some of them are applied to formulate the necessary and sufficient condition for a hereditary radical 𝒫 and its supplementing radical 𝒫′ forming a dual pair.     

Associated radical ideals of monomial ideals

Algebraic and combinatorial properties of a monomial ideal are studied in terms of its associated radical ideals. In particular, we present some applications to the symbolic powers of square-free monomial ideals.     

The normalizer property of integral group rings of semidirect products of finite 2-closed groups by rational groups

Let G = N?Q be a semidirect product of a finite 2-closed group N by a rational group Q. It is shown that under some conditions the normalizer property holds for G.     

New criterion of the approximation property

This paper is concerned with the approximation property which is an important property in Banach space theory. We show that a Banach space X has the approximation property if (and only if), for every Banach space Y, the set of finite rank operators from X to Y is dense in the corresponding space of compact operators, in the usual topology of uniform convergence on compact sets.     

A property of Dunford-Pettis type in topological groups

The property of Dunford-Pettis for a locally convex space was introduced by Grothendieck in 1953. Since then it has been intensively studied, with especial emphasis in the framework of Banach space theory.

In this paper we define the Bohr sequential continuity property (BSCP) for a topological Abelian group. This notion could be the analogue to the Dunford-Pettis property in the context of groups. We have picked this name because the Bohr topology of the group and of the dual group plays an important role in the definition. We relate the BSCP with the Schur property, which also admits a natural formulation for Abelian topological groups, and we prove that they are equivalent within the class of separable metrizable locally quasi-convex groups.

For Banach spaces (or for metrizable locally convex spaces), considered in their additive structure, we show that the BSCP lies between the Schur and the Dunford-Pettis properties.

     

Serre''s contribution to the development of algebraic topology

We describe in detail Serre's application of spectral sequence theory to the study of the relations between the homology of total space, base space and fibre in a Serre fibration; and we apply the results to establish that a 1-connected space X has homology groups (in positive dimension) in a Serre class C if and only if its homotopy groups are in C.

We include in this paper some personal reflections on the contact the author had with Serre during the decade of the 1950's when Serre's revolutionary work in homotopy theory was completely changing the face of algebraic topology.     

The Reznichenko property and the Pytkeev property in hyperspaces

Summary We investigate two closure-type properties, the Reznichenko property and the Pytkeev property, in hyperspace topologies.     

FPF环和AUT-PIC性质

设R是—FPF环（不要求交换），本文研究了R的一些性质并给出了R上的有限生成投射左R-模的两种直和分解．在本文的第三部分，我们证明了以下结果：（a）FPF环具有Aut－Pic性质．（b）R有Aut-Pic性质当且当R／I有Aut－Pic性质，I是R的根式理想．（c）作为Aut－Pic性质的一个应用，定理3.3推广了[9]中的一个结果．     

The product replacement algorithm and Kazhdan's property (T)

The ``product replacement algorithm' is a commonly used heuristic to generate random group elements in a finite group , by running a random walk on generating -tuples of . While experiments showed outstanding performance, the theoretical explanation remained mysterious. In this paper we propose a new approach to the study of the algorithm, by using Kazhdan's property (T) from representation theory of Lie groups.