PSL（2，F）的一个嵌入定理及其应用

设Ｆ是任意域，Ｇ代表ＳＬ（２，Ｆ）或ＰＳＬ（２，Ｆ）．本文的主要结果是：设Ｋ是Ｆ的子域，则Ｇ中同构于ＳＬ（２，Ｋ）或ＰＳＬ（２，Ｋ）的子群在Ｇ的自同构的作用下彼此共轭，利用这一结果，本文明确确定了A₁^[1]型的仿射Ｋａｃ－Ｍｏｏｄｙ群的一类极大正规子群．     

一类特殊广义Kac—Moody代数虚根决定的反射与Weyl群间的关系

对有限型李代数ｇ（Ａ）,相应于每个根ａ的反射ｒａ均在ｇ（Ａ）的Ｗｅｙｌ群Ｗ中,当ｇ（Ａ）为可对称化的不定型Ｋａｃ－Ｍｏｏｄｙ代数时,若ａ为一虚根且（ａ,ａ）〈０,则亦可定义反射ｒａ,并有ｒａ∈－Ｗ或ｒａ是－Ｗ中元与一个图自同构之积,本文给出了一类秩为３的广义Ｋａｃ－Ｍｏｏｄｙ代数的虚根系,然后讨论了一类特殊的广义Ｋａｃ－Ｍｏｏｄｙ代数的虚根决定的反射与Ｗｅｙｌ群之间的关系。     

可积模的权

本文定义了Ｋａｃ－Ｍｏｏｄｙ代数的一个新的可积模范畴，并且给出了一个可积模是否属于这个模范畴的一个判别准则．另外还详细研究了这个模范畴中的可积模的权系。特别我们定义了虚权和实权。还详细地计算了一些模的虚权和实权，还给出了双曲型广义Ｃａｒｔａｎ矩阵的新刻划．这使我们能够计算一些双曲型Ｋａｃ－Ｍｏｏｄｙ代数的可积模的权。     

关于G-Matlis自反模的换环定理

设Ｒ和Ｔ是Ｎｏｅｔｈｅｒ完备半局部环，Ｒ→Ｔ是环同态．本文证明了，若Ｔ是有限生成或ＡｒｔｉｎＲ－模，Ｍ为Ｇ－Ｍａｔｌｉｓ自反Ｒ－模，则对所有ｎ≥０，Ｅｘｔ^Ｒ_ｎ（Ｔ，Ｍ），Ｅｘｔ^Ｒ_ｎ（Ｍ，Ｔ），Ｔｏｒ^Ｒ_ｎ（Ｔ，Ｍ）以及Ｔｏｒ^Ｒ_ｎ（Ｍ，Ｔ）均是Ｇ－Ｍａｔｌｉｓ自反Ｔ－模．所得结果推广了Ｒ．Ｂｅｌｓｈｏｆ的结果．     

内—p—闭群及其推广

非ｐ—闭群Ｇ叫拟ｐ—闭群，如果有Ｇ的真子群Ｈ，当(?)时．Ｋ就是ｐ—闭群。本文证明了下列定理：定理１拟ｐ—闭群有下述二型：Ⅰ当Ｇ可解时，２≤｜π（Ｇ）｜≤３。Ⅱ当Ｇ不可解时，ａ）Ｇ／Φ（Ｇ）为复阶单群。ｂ）(?)为复阶单群。定理２内—５—闭群有下述二大类型：Ⅰ ５^αｐ^β阶ｐ—基本群。Ⅱ Ｇ／Φ（Ｇ）同构于ＰＳＬ（２，５），Ｓ_ｚ（２^ｑ）（ｑ为奇素数）     

H*－有理模和右Smash积A＃HRH*

本文对Ｈ^*上的有理模Ｍ做了一些讨论，刻划了此类模的某些性质，并利用这些性质得到了右Ｓｍａｓｈ积Ａ＃_H^R［ｋＧ］^*上模Ｍ是完全可约模的条件。     

Structures of Wey1 Groups of Some Kac-Moody Algebras

ＳｔｒｕｃｔｕｒｅｓｏｆＷｅｙ１ＧｒｏｕｐｓｏｆＳｏｍｅＫａｃ┐ＭｏｏｄｙＡｌｇｅｂｒａｓ＊）ＬｕＣａｉｈｕｉ（卢才辉）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣａｐｉｔａｌＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ，１０００３７）Ｚ...     

三角形蛇图的调和性

称有ｅ条边的简单图Ｇ为调和图，若存在单射ｈ：Ｖ（Ｇ）→Ｚ_ｅ，Ｚ_ｅ是模ｅ的整数群，其导出映射ｈ^*：Ｅ（Ｇ）→Ｚ_ｅ；ｈ^*（ｖｖ）≡ｈ（ｎ）＋ｈ（ｖ）（ｍｏｄｅ），ｎ，ｖ∈Ｖ（Ｇ）是一个双射，称ｈ为Ｇ的一个调和标号三角形蛇图是一个其所有块都是三角形且其块－割点图为一条路的连通图。本文证明了具有ｔ个块的三角形蛇图足调和的，当且仅当ｔ≠２（ｍｏｄ４）。     

A NEW REGULARITY CLASS FOR THE NAVIER-STOKES EQUATIONS IN IR~n

ＡＮＥＷＲＥＧＵＬＡＲＩＴＹＣＬＡＳＳＦＯＲＴＨＥＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮＳＩＮＩＲ~ｎ￥Ｈ．ＢＥＩＲａＯＤＡＶＥＩＧＡ（ＤｅｐｏｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＰｉｓａＵｎｉｖｅｒｓｉｔｙ，Ｐｉｓａ，Ｉｔａｌｙ）Ａｂｓｔｒａ?..     

关于分次本质右理想

设 Ｒ是 Ｇ－分次,本文讨论了环 Ｒ的相关环 Ｒ,Ｒ＃ Ｇ^*, Ｒｅ, Ｑ（Ｒ）, Ｒ^G, Ｒ*Ｇ及 Ｒ的正规化扩张Ｓ的非奇异性,右一致性,右基座之间的关系．当Ｒ_Ｒ是ＹＪ－内射模时,证明了Ｊ（Ｒ）＝Ｚ（Ｒ）。     

Some Properties of Bell Groups

For any integer n ≠ 0,1, a group G is said to be “n-Bell” if it satisfies the identity [x ⁿ ,y] = [x,y ⁿ ]. It is known that if G is an n-Bell group, then the factor group G/Z ₂(G) has finite exponent dividing 12n ⁵(n ? 1)⁵. In this article we show that this bound can be improved. Moreover, we prove that every n-Bell group is n-nilpotent; consequently, using results of Baer on finite n-nilpotent groups, we give the structure of locally finite n-Bell groups. Finally, we are concerned with locally graded n-Bell groups for special values of n.     

Characterization of 3-Rewritable Finite Nilpotent Groups

Let n be an integer greater than 1. A group G is said to be “ n-rewritable” whenever for every n elements x ₁,…,x _n of G, there exist distinct permutations τ, σ on the set {1,2,…, n} such that x _τ(1) ··· x _τ(n) = x _{σ (1)} ··· x _{σ (n)}. In this article, we complete the classification of 3-rewritable finite nilpotent groups and prove that a finite nilpotent group G is 3-rewritable if and only if G has an abelian subgroup of index 2 or the derived subgroup has order < 6.     

3-Rewritable Nilpotent 2-Groups of Class 2#

ABSTRACT

Let n be an integer greater than 1. A group G is said to be n-rewritable (or a Q_n-group) if for every n elements x₁, x₂,…,x_n in G there exist distinct permutations σ and τ in S_n such that x_σ(1)x_{σ (2)} ??? x_σ(n) = x_τ(1)x_τ(2) ??? x_τ(n). In this paper, we characterize all 3-rewritable nilpotent 2-groups of class 2. Also we have found a bound for the nilpotency class of certain nilpotent 3-rewritable groups, and have shown that 3-rewritable groups satisfy a certain law.     

On linearity of finitely generated R-analytic groups

In this paper we prove that if R is a commutative Noetherian local pro-p domain of characteristic 0, then every finitely generated R-standard group is linear. This work has been partially supported by the FEDER, the MEC Grant MTM2004-04665 and the Ramón y Cajal Program.     

On Hypercentral Groups G With |G:G n |<∞

In 1960, Baumslag, following up on work of Cernikov for the 1940s, proved that a hypercentral p-group G with G = G ^p is a divisible Abelian group. In this article, we provide an interesting generalization of this 45 year old result: If a hypercentral p-group G satisfies |G:G ^p |<∞ (of course, it contains G = G ^p ), there exists a normal divisible Abelian subgroup D such that |G:D|<∞.     

A decomposition theorem for G-groups

Some classical results about linear representations of a finite group G have been also proved for representations of G on non-abelian groups （G-groups）. In this paper we establish a decomposition theorem for irreducible G-groups which expresses a suitable irreducible G-group as a tensor product of two projective G-groups in a similar way to the celebrated theorem of Clifford for linear representations. Moreover, we study the non-abelian minimal normal subgroups of G in which this decomposition is possible.     

COMPLETENESS OF THE PARABOLIC SUBGROUPS OF PROJECTIVE ORTHOGONAL GROUPS

All parabolic subgroups and Borel subgroups of PΩ(2m 1, F) over a linear-able field F of characteristic 0 are shown to be complete groups, provided m > 3.     

Bestvina's Normal Form Complex and the Homology of Garside Groups

A Garside group is a group admitting a finite lattice generating set . Using techniques developed by Bestvina for Artin groups of finite type, we construct K(π, 1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice , and there is a simple sufficient condition that implies G is a duality group. The universal covers of these K(π, 1)s enjoy Bestvina's weak nonpositive curvature condition. Under a certain tameness condition, this implies that every solvable subgroup of G is virtually Abelian.