关于某些多边形积的剩余有限性

讨论嵌入子群是循环群的有限p-群的多边形积,得到了多边形积为剩余有限的一个充分条件.     

剩余格的弱布尔积表示

在剩余格L中,首先证明了因子同余是由布尔元所唯一生成的,继而证明了由B(L)的素滤子诱导的商代数是直不可分解的.其次,给出了剩余格L的弱布尔积表示,并证明了伴随表示的等价性.最后,证明了剩余格L的序素谱与其stalks的素谱基数和序同构.     

某些无限幂零群的剩余有限性质

研究了无限幂零群的剩余有限性质, 得到了 群的一些幂零性条件     

无限可解群的强剩余有限性

本文讨论了无限可解群的强剩余有限性,证明了一个 o-群G是强剩余有限的当且仅当G的谱Sp(G)是个空集.这包含了Malcev关于多重循环群的一项有名工作.     

无限可解群的强剩余有限性

本文讨论了无限可解群的强剩余有限性,证明了一个 0-群G是强剩余有限的当且仅当G的谱Sp（G）是个空集.这包含了Malcev关于多重循环群的一项有名工作.     

关于剩余有限群的Profinite完备化

设G是个剩余有限群,本文深入地讨论了G的Profinite完备化之间的关系,得到了整齐的结     

关于剩余有限群的Profinite完备化

设G是个剩余有限群,本文深入地讨论了G的Profinite完备化之间的关系,得到了整齐的结果.     

关于有限群两个幂零子群积的问题

众所周知,有限群的两个幂零子群的积不一定是幂零的．本文研究了Ｅｎｇｅｌ条件对两个幂零子群的影响,得到两个幂零子群的积为幂零群的几个充分条件。     

关于有限群两个超可解子群之积的问题

In this paper, we give some sufficient conditions for products of two supersolvable sub-groups to be supersolvable groups. Our results generalize some known results.Theorem 1 Let G = HK,(|H|,|K|) = 1, Where H and K are two supersolvable sub-groups. If H is commutative with every maximal subgroup of K, and K is commutative with every maximal subgroup of H, then G is supersolvable.Theorem 2 Let G = HK, H ∩ K = 1, H G, and K be quasinormal in H. If H, K are supersolvable, the G is supersolvable.Theorem 3 Let G= HK,(|H|,|K|) = 1,H,K be two supersolvable subgroups. If H is commutative with any Sylow subgroup of K and any maximal subgroup of every sylow subgroup of K, and K is commutative with any sylow subgroup of H and any maximal subgroup of every sylow subgroup of H, then G is supersolvable. Theorem 4 If H,K are two supersolvable subgroups of G, G= HK, G′is nilpotent, H is quasi normal K, and K is quasi normal in H,then G is supersolvable. Theorem 5 If H,K are two supersolvable subgroups of G, G= HK, H′? G,[H,K]? G,[H,K] is nilpotent, H is quasi normal in K, and K is quasi normal in H,then G is supersolvable.     

关于多边形分平面区域的计数问题

平面区域的计数问题是组合数学中的一个专题 .本文将利用递推函数的方法来讨论ｎ个开放图形或ｎ个封闭图形分平面所得到的最多区域数的问题 .首先给出封闭图形和开放图形的概念 :封闭图形 :指一般的凸ｎ边形 ;如 ,三角形、四边形 .开放图形 :指在凸ｎ边形中去掉ｍ条边 (ｎ-2 ≥ｍ≥ 1 ) ,如果可以把被去掉的边的端点在图中相关的线段改为射线或直线 ;如 ,一组平行线、角ＡＯＢ .其中每一条直线、线段或射线都称为边 .定理 1　ｎ个角 (这里只讨论锐角的情况 )最多把平面分成 2ｎ2 -ｎ +1个区域 .分析　当ｎ个角把平面分成的区域数最多时 ,这…     

On residual finiteness of direct products of algebraic systems

It is well known that if two algebraic structures A and B are residually finite then so is their direct product. Here we discuss the converse of this statement. It is of course true if A and B contain idempotents, which covers the case of groups, rings, etc. We prove that the converse also holds for semigroups even though they need not have idempotents. We also exhibit three examples which show that the converse does not hold in general.      

多边形链图中的完美匹配数

多边形链图的完美匹配数（即多边形碳氢链状聚合物的Ｋｅｋｕｌｅ结构数）是数学化学研究的重要内容之一。我们给出了一个求该数的简洁算法,并证明该数是一个多项式。做为应用,对于一类特殊的多边形链图,给出了具体的表达式。     

Groups with Conditions of Finiteness

A review of V. P. Shunkovs research on groups with conditions of finiteness is given. Memories of the beginning of his scientific career are recalled. The work is supported by the Russian Fund of Fundamental Researches (grant 02-01-00078).Mathematics Subject Classification (2000) 20E99.     

Finiteness of mapping degree sets for 3-manifolds

By constructing certain maps, this note completes the answer of the question: For which closed orientable 3-manifold N, is the set of mapping degrees D(M,N) finite for any closed orientable 3-manifold M?     

On the Residual Solvability of Generalized Free Products of Finitely Generated Nilpotent Groups

In this article we study the residual solvability of the generalized free product of finitely generated nilpotent groups. We show that these groups are often residually solvable.     

某些无穷乘积的超越性

本文给出某些用无穷乘积表示的函数在代数点和超越点上的值的超越性．     

一类多重循环群的剩余有限性质

设A是秩为n(n≥2)的自由Abel群,A的自同构群Aut(A)= GL(n,Z).对整数m,取 α =(0 1 0…0 0 0(………)(…………)0 0 0…0 1 1 0…0 m)∈ Aut(A).记Γm(n)=A(×)〈α〉,则它是一个2元生成的多重循环群.本文给出了 Γm(n)的准确的剩余有限性质.     

On the Residual Finiteness of Outer Automorphisms of Hyperbolic Groups

We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable hyperbolic group is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated Fuchsian group and of every free-by-finite group is residually finite.