A_2(F)在G_2(F)中的扩群及其泛正规性

域Ｆ上Ａ２型Ｃｈｅｖａｌｌｅｙ群Ａ２（Ｆ）可视为Ｆ上Ｇ２型Ｃｈｅｖａｌｌｅｙ群Ｇ２（Ｆ）的子群．当 Ｆ是特征不为 ２，３的域且 Ｆ＝Ｆ３时，本文给出了 Ａ２（Ｆ）在 Ｇ２（Ｆ）中的所有扩群及其泛正规性．     

A class of exceptional bernstein algebras associated to graphs1

Given a simple graph G without loops and a field F of characteristic not 2 wr construct an exceptional Bernstein algebra F(G)over F and show that F(G)is indecomposable if and only if G is connected. The duplicate of F(G) is a Bernstein Jordan algebra whose type is deter- mined by the number of points and lines of G. We comment briefly how to extend the theory to the case of multigraphs.     

Generalized Schur-concave Functions and Eaton Triples

Motivated by Schur-concavity, we introduce the notion of G -concavity where G is a closed subgroup of the orthogonal group O ( V ) on a finite dimensional real inner product space V . The triple ( V , G , F ) is an Eaton triple if F ² V is a nonempty closed convex cone such that (A1) Gx 7 F is nonempty for each x ε V . (A2) max g ε G ( x,gy ) = ( x,gy ) for all x, y ε F . If W := span F and H := { g | W : g ε G , gW = W } ² O ( W ), and ( W , H , F ) is an Eaton triple, then ( W , H , F ) is called a reduced triple of the Eaton triple ( V , G , F ). In this event, a characterization of the G -concavity in terms of H -concavity is obtained. Some differential characterizations of G -concavity are then given. The results are applied to Lie groups. Various matrix examples are given.     

C~*-index of observable algebras in G-spin model

In two-dimensional lattice spin systems in which the spins take values in afinite group G,one can define a field algebra F which carries an action of a Hopf algebraD(G),the double algebra of G and moreover,an action of D(G;H),which is a subalgebraof D(G)determined by a subgroup H of G,so that F becomes a modular algebra.Theconcrete construction of D(G;H)-invariant subspace A_H in F is given.By constructingthe quasi-basis of conditional expectation γ_G of A_H onto A_G,the C~*-index of γ_G is exactlythe index of H in G.     

On commutative group algebras of mixed groups

Suppose F is a perfect field of characteristic p 0 and G is an abelian group whose torsion subgroup Gt is p-primary. If Gt is totally projective of countable length, it is shown that G is a direct factor of the group of normalized units V(G) of the group algebra F(G) and that V(G)/G is a totally projective p-group. The proof of this result is based on a new characterization of the class of totally projective p-groups of countable length. Li addition, the same result regarding V(G) is obtained if G has countable torsion-free rank and Gt is totally projective of length less than ω₁ + ω₀ . Finally, these results are applied to the question of whether the existence of an F-i pomorphism F(G) ? F(H) for some group H implies that G?H.     

有限群的最大子群的性质对群结构的影响

有限群G的一个子群称为在G中是π-拟正规的若它与G的每一个Sylow-子群是交换的.G的一个子群H称为在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).本文证明了:设F是一个包含超可解群系u的饱和群系,G有一个正规子群H使得G/H∈F.则G∈F若下列之一成立:(1)H的每个Sylow子群的所有极大子群在G中或者是π-拟正规的或者是c-可补的;(2)F*(H)的每个Sylow子群的所有极大子群在G中或者是π-拟正规的或者是c-可补的,其中F*(H)是H的广义Fitting子群.此结论统一了一些最近的结果.     

序列平行图的最小填充

起源于稀疏矩阵计算和其它应用领域的一个图G的最小填充问题就是在G中寻找一个边数| F |最小的添加边集F,使得G+F是弦图.这里最小值| F |称为图G的填充数,表示为f(G).对一般图来说,这个问题是NP-困难问题.一些特殊图类的最小填充问题已被研究.本文给出了序列平行图G的最小填充数的具体值.     

阿贝尔群被超-(循环或有限)群的可裂扩张(Ⅰ)

设F是由f(p)所局部定义的可解群系,G∈F,A是ZG-模.我们称A的一个p-主因子U/V在G中是F-中心的,如果G/CG(U/V)∈f(p).否则称U/V在G中是非中心的.本文证明了:设G是超-(有限或循环)的局部可解群,A是Artinian ZG-模且所有的不可约ZG-因子都是有限的;F为由f(p)所局部定义的局部可解群系,且对任意的p∈π,f(p)≠φ,f(∞) f(p).如果G∈F,且A的所有不可约ZG-因子在G中均是F-非中心的,则A被G的扩张在A上共轭可裂..     

Formations and Products of F(G)-Subnormal Subgroups of Finite Solvable Groups

Mathematical Notes - A subgroup H of a finite group G is said to be F(G)-subnormal if it is subnormal in HF(G), where F(G) is the Fitting subgroup of G. In the paper, the problem of whether or not...     

简化图的一个注记

本文研究了F(G)=3时简化图的性质.利用收缩法,给出了简化图G当F(G)=3时的两个性质.作为应用,也给出了具有至多10个3度点的3边连通的简化图的一个性质.推广了Catlin和Lai等人的一些关于F(G)≤2的结果.     

The Minimum FIll—in for the Corona of Two Graphs

Ｔｈｅ　Ｍｉｎｉｍｕｍ　Ｆｉｌｌ－ｉｎ　ｆｏｒ　ｔｈｅ　Ｃｏｒｏｎａ　ｏｆ　Ｔｗｏ　ＧｒａｐｈｓＴｈｅＭｉｎｉｍｕｍＦｉｌｌ－ｉｎｆｏｒｔｈｅＣｏｒｏｎａｏｆＴｗｏＧｒａｐｈｓ￥ＪｉｎＺｈｉｙｏｎｇ；ＬｉＷｅｎｑｕａｎ（ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ...     

Locally nilpotent groups with a centralizer of finite rank

Locally nilpotent groups in which the centralizer of some finitely generated subgroup has finite rank are studied. It is shown that if G is such a group and F is a finitely generated subgroup with centralizer C_G(F) of finite rank, then the centralizer of the image of F in the factor group G/t(G) modulo the periodic part t(G) also has finite rank. It is also shown that G is hypercentral when F is cyclic and either G is torsion-free or all Sylow subgroups of the periodic part of C_G(F) are finite.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 11, pp. 1511–1517, November, 1992.     

二值命题逻辑中理论的发散性、相容性及其拓扑刻画

在二值命题逻辑系统中基于逻辑度量空间(F(S),ρ)而建立起了逻辑理论的发散性、相容性和理论的拓扑性质之间的联系。证明了逻辑理论Г是全发散的当且仅当D(Г)在(F(S),ρ)中稠密,闭理论Г是相容的当且仅当Г在(F(S),ρ)中不含内点,证明了(F(S),ρ)是零维空间,并具有一种类似于樊畿性质的所谓“有限等球连通性”．     

A New Type of Pronormal Subgroups in Chevalley Groups

Let L be a simple Lie algebra with irreducible root system φ having roots of different length,F be a field of characteristic different from 2,G=L(F) be a Chevalley group of type L over F.Denote by φ^1 the set of all long roots in φ.Set G^1=(zr(t);r∈φ^t,t∈F).It is a subgroup of G generated by all the long root subgroups.This paper determines the pronormality of G^1 in G when L is not of type G2.     

Connections between projective geometry and superassociative algebra

This paper establishes a connection between projective geometry and the superassociative algebra of multiplace functions. In Part I a quaternary operation is defined for the points on a line j in a projective plane π relative to a fixed quadrangle and the result of operating on A,B,C,D is denoted by A(B,C,D). It is shown that π is a Pappus plane if and only if this operation is superassociative: (A(B,C,D))(E,F,G)=A(B(E,F,G),C(E,F,G),D(E,F,G)) for any points A,B,C,D,E,F,G on j. Desargues and certain special Desargues planes are also characterized by restrictions of the superassociative law. In Part II projective geometry is developed over superassociative systems.     

On principal invariant subspaces

Let F and G be closed subspaces of the complex Hilbert space H, and U and V be closed subspaces of F and G, respectively. In this paper, using the technique of operator block, we present the necessary and sufficient conditions under which (U, V) is a pair of (strictly, non-degenerate) principal invariant subspaces for (F, G).     

Maximal Subgroups in the Classical Groups Normalizing Solvable Subgroups

Let G be a classical group over an arbitrary field F,acting on an n-dimensional F-space V=V(n,F).All those maximal subgroups of G are classified each of which normalizes a solvable subgroup N of GL(V/F)not lying in F*1v.     

图中推广的正交因子分解

设G是一个图,具有顶点集合V(G)和边集合E(G).设g和f是定义在V(G)上的整数值函数,使对每个x∈V(G),有g(x)≤f(x).图G的一个(g,f)-因子是G的一个支撑子图H,使对每个x∈V(G),有g(x)≤d_H(x)≤f(x).G的一个(g,f)-因子分解是E(G)的边不相交的(g,g)-因子的一个划分.设F={F-1,F_2,…,F_m}为G的一个因子分解,H是G的一个有mr条边的子图.如果每个F_i恰好与H有r条公共边,1≤i≤m,则称Fr-正交于H.本文证明每个(mg+kr,mf-kr)-图含有一个子图R,使R有(g,f)-因子分解r-正交于任意给定的有kr条边的子图,其中m,k和r为正整数且k相似文献   

弦图的补图的最小填充

从图论观点讲,最小填充问题就是在一个图G中添加边集F,使得图G的母图G F是一个弦图而且所添边的边数| F|是最小的,其中最小值| F|称为图G的填充数,表示为f( G) .对一般图来说,最小填充问题是NP-困难的,但是对一些特殊图类来说,这个问题是在多项式时间内可解的.本文给出了弦图的补图-G的填充数f(-G) .