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1.
关于l-群的半单结构 总被引:4,自引:0,他引:4
令G是一个l-群,G的一个凸l-子群A叫做多余的,如果对G的任-凸l-子群W,只要A∨W=G,就有W=G.复令R(G)为G的所有多余凸l-子群的集合并生成的凸l-子群.我们证明了R(G)是l-群G的一种报并且是在Amitsur-Kurosh意义下的根.进一步我们得到了有限值l-群的半单结构定理即R(G)=0当且仅当Gl-同构于具有半单性的单l-群的亚直积,同时我们还得到了一系列有意义的推论. 相似文献
2.
本文证明了如下结论:(1)若有限群G的一个Hallπ-子群H在GF内是S-半正规的,则H在G内有补且所有这样的补在G中互相共轭,(2)令P/G/,若有限群G的Sylowp-子群在G内是S-半正规的,则G是p-可解的;(3)如果G与PSL(2,7)是无关的,则G是π-可分的;(4)令P是一个奇素数,则其每个极小P-子群一S-半正规的有限群G-一定是P=超可解的。 相似文献
3.
本文研究了C-根类(即凸l-子群格可分辨根类)和K-根类.证明了:投射l-群、强投射l-群、两两分裂l-群、F-群等许多l-群类都是l-子群格可分辨的,但Hamiltonl-群不是;C-根类格是根类格的一个有伪补的闭子格,而且是根类半群的一个子半群.每个凸O一子群都是闭的,而且给出了由一簇K一根类及一个根类所生成的K-根类的形式. 相似文献
4.
本文给出了有限交换局部环R上无限线性群GL(R)=∪nGLnR的Sylowp-子群的形式.令M是有限交换局部环R的唯一极大理想,k=R/M为R的剩余类域.用X(k)表示k的特征,并假定P与x(k)互素.作者证明了:GL(R)的任一Sylowp-子群S或者同构于的可数无限直积与P(j)的无限直积的直积(当P≠2或P=2,X(k)β≡1(mod4))或者同构于Pi的无限直积与P(j)的无限直积的直积(当P=2,X(k)β≡3(mod4)),这里,只是GL(epi)R(分别地,GL(2ri)R)的Sylowp-子群,P(j))同构于P=∪i∈Ipi,I是可数集. 相似文献
5.
分次Morita对偶,Morita对偶与Smash积 总被引:1,自引:0,他引:1
设C和r都是群,是G-型分次环,是Γ-型分次环.是双分次模,R#G是R的Smash积,A#Γ是A的Smash积。令W=(_gU_(σ-1))_(g,σ)即(g,σ)位置取_gU_(σ-1)的元素的|G|×|Γ|矩阵的全体组成的集合,且每个矩阵的每行和每列的非零元只有有限个,按矩阵运算,W构成(R#6,A#Γ)双模。则_RU_A定义了一个分次Morita对偶当且仅当_(R#G)W_(A#Γ)定义了一个Morita对偶。 相似文献
6.
同无限二面体群关联的晶体群的分类 总被引:3,自引:1,他引:2
设V是实数域R}上的一个2-维向量空间,V带有一个仿射的或不定的对称双线性型.无限二面体群W能够被看作GL(V)的一个子群.在本文中,在仿射群A(V)中共轭的意义下将分类同W关联的所有晶体群. 相似文献
7.
王殿军 《数学年刊A辑(中文版)》1995,(1)
设G是有限群,πs(G)为G的极大子群阶之集.本文证明了若q=pn>2,p素,则G≌L2(q)当且仅当πs(G)=πs(L2(q)).对一些其它的单群也证明了同样的结论. 相似文献
8.
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 相似文献
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10.
有限交换环上线性群的Carter子群 总被引:2,自引:0,他引:2
令R为有限交换局部环,K为其剩余类域.本文研究了R上一般线性群GLnR的Carter子群的存在性及结构.得到的结果是:若charK为奇数或K=F2,GLnR中存在唯一的Carter子群的共轭类,即Sylow-2子群的正规化子;若charK=2且|K|>2,GLnR中不含Carter子群. 相似文献
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12.
N. Ya. Medvedev 《Algebra and Logic》2005,44(3):197-204
A sufficient condition is given under which factors of a system of normal convex subgroups of a linearly ordered (l.o.) group are Abelian. Also, a sufficient condition is specified subject to which factors of a system of normal convex subgroups of an l.o. group are contained in a group variety
. In particular, for every soluble l.o. group G of solubility index n, n ⩾ 2, factors of a system of normal convex subgroups are soluble l.o. groups of solubility index at most n − 1. It is proved that the variety
of all lattice-ordered groups, approximable by linearly ordered groups, does not coincide with a variety generated by all soluble l.o. groups. It is shown that if
is any o-approximable variety of l-groups, and if every identity in the group signature is not identically true in
, then
contains free l.o. groups.Supported by FP “Universities of Russia” grant UR. 04. 01. 001.__________Translated from Algebra i Logika, Vol. 44, No. 3, pp. 355–367, May–June, 2005. 相似文献
13.
Tin-Yau TAM 《Linear and Multilinear Algebra》2013,61(2):113-120
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. 相似文献
14.
S. A. Gurchenkov 《Algebra and Logic》1995,34(4):219-222
An Engel l-group generating a proper normal-valued l-variety is shown to be o-approximable. It is also established that for every proper normal-valued l-varietyF, the class (F) of Engel l-groups from F is a torsion class.Translated fromAlgebra i Logika, Vol. 34, No. 4, pp. 398–404, July-August, 1995. 相似文献
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16.
S. A. Gurchenkov 《Algebra and Logic》1996,35(3):149-159
We deal with varieties of lattice-ordered groups {ie149-1} defined by the identity [xn, yn]=e. The structure of subdirectly indecomposable l-groups in the variety {ie149-2} is studied, and we establish that l-varieties
satisfying the identity [xn, yn]=e and generated by a finitely generated l-group are finitely based. It is shown that l-varieties {ie149-3} with finite axiomatic
rank {ie149-4} also have finite bases of identities.
Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 268–287, May–June, 1996. 相似文献
17.
半二面体群的小度数Cayley图 总被引:1,自引:0,他引:1
群G的一个Cayley图X=Cay(G,S)称为正规的,如果右乘变换群R(G)在Aut X中正规.研究了4m阶半二面体群G=〈a,b a2m=b2=1,ab=am-1〉的3度和4度Cayley图的正规性,其中m=2r且r>2,并得到了几类非正规的Cayley图. 相似文献
18.
The pure-dimer problem was solved in exact closed form for many lattice graphs. Although some numerical solutions of the monomer–dimer problem were obtained, no exact solutions of the monomer–dimer problem were available (except in one dimension). Let G be an arbitrary graph with N vertices. Construct a new graph R ( G ) from G by adding a new verex e * corresponding to each edge e = ( a , b ) of G and by joining each new vertex e * to the vertices a and b . If the suitable activities of vertices and edges in R ( G ) are selected, then the monomer–dimer problem can be solved exactly for the graph R ( G ), which generalizes the result obtained by Yan and Yeh. As applications, if we select suitable activities for the vertices and edges of , we obtain the exact formulae for the MD partition function, MD free energy, and MD entropy of for the d -dimensional lattice with periodic boundaries. 相似文献
19.
群G的一个Cayley图X=Cay(G,S)称为正规的,如果右乘变换群R(G)在AutX中正规.研究了4m阶拟二面体群G=a,b|a~(2m)=b~2=1,a~b=a~(m+1)的4度Cayley图的正规性,其中m=2~r,且r2,并得到拟二面体群的Cayley图的同构类型. 相似文献
20.
We argue that for any subgroup H of rank 1 in a multiplicative group of positive reals, among Dlab groups of the closed intervalI=[0],[1] on an extended set
of reals, there exist groups DH*(I) and DH* which lack normal relatively convex subgroups, are not simple groups, and have just two distinct linear orders. The cardinality
of a set of linear orders on Dlab groups is computed. It is established that every rigid l-group is Abelian if it belongs
to a varietyD of l-groups groups generated by the linearly ordered groups DH*(I) and DH*. We prove that the quasivariety q(DH*(I), DH*) of groups generated by DH*(I) and DH* is distinct from a quasivarietyO of all orderable groups. Similar results are stated for a variety of l-groups and the quasivariety of groups that are not
embeddable in DH*(I) and DH*.
Supported by RFFR grant No. 96-01-00088.
Translated fromAlgebra i Logika, Vol. 38, No. 5, pp. 531–548, September–October, 1999. 相似文献