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1.
本文研究了单值群的可解性与Fuchsian方程可积性之间的关系.利用可解群及GL(n,K)的性质,获得GL(n,K)中一类准可解子群的结构定理,并将之心用于Fuchsian系统的可积性研究之中.  相似文献   

2.
有限交换环上线性群的Carter子群   总被引:2,自引:0,他引:2  
游宏 《数学学报》1998,41(4):773-778
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   

3.
李尚志 《数学学报》1990,33(6):774-778
设 F 是任意域.当 K 是 F 的子域且[F:K]<(?)时,或当 K 是 F 的极大子环但不是域时,本文定出了 SL(n,K)在 GL(n,F)中的全部扩群,从而得出了 SL(n,F)的一类极大子群.  相似文献   

4.
有限群极大子群的θ-子群偶   总被引:21,自引:0,他引:21  
赵耀庆 《数学学报》1997,40(1):67-72
N.P.Mukherjee和 P.Bhattacharya在“On theta pairs for a maximal sub-group”(Proc.Amer.Math.Soc,Vl09N3(1990))一文中定义了有限群的极大子群的θ-子群偶概念,研究了极大子群的极大θ-子群偶对群结构的影响,得到了一系列结果.本文在进一步探究θ-子群偶性质的基础上,对该文中一系列主要结果作出了本质性的改进,并给出了可解性、幂零性的一些新刻划.  相似文献   

5.
有限群极大子群的正规指数   总被引:6,自引:0,他引:6  
郭秀云 《数学学报》1991,34(2):208-212
对于有限群G的极大子群M,定义M的正规指数为G的主因子H/K的阶,这里H是M在G中的极小正规补。在这篇注记中,使用正规指数这一概念我们获得了有限群为p-可解,可解,超可解的一些充分必要条件。  相似文献   

6.
有限群的s-条件置换子群   总被引:15,自引:0,他引:15  
如果对群G的任意Sylow子群T,存在一个元素x∈G,使得HTx=TxH,那么称群G的子群H在G中s-条件置换.利用s-条件置换子群给出了一些群的性质和结构.  相似文献   

7.
如果对群G的任意Sylow子群T,存在一个元素x∈G,使得HT~x=T~xH,那么称群G的子群H在G中s-条件置换.利用s-条件置换子群给出了一些群的性质和结构.  相似文献   

8.
非幂零极大子群指数为素数幂的有限群   总被引:7,自引:0,他引:7  
本文证明了如下结果,1.设p是一个素数,如果有限群G的每一非幂零的极大子群的指数都为p的方幂,则G为可解群.2.如果有限群G的每一非幂零的极大子群的指数为素数幂,则G/S(G)1或PSL(2,7),其中S(G)表示G的最大可解正规子群.  相似文献   

9.
Sylow子群的极大子群在局部子群中的 π - 拟正规性   总被引:3,自引:0,他引:3  
有限群 G 的一个子群 H 称为在 G 中 π - 拟正规的, 如果 H 和G的每一个Sylow子群可交换. 自从这一概念被 Kegel 提出后, 许多学者相继研究了某些子群在G中的 π - 拟正规性对有限群结构的影响.该文将上述条件局部化,即在群 G 的Sylow 子群的正规化子中来研究这一性质与有限群结构之间的关系.  相似文献   

10.
有限群极大子群的强θ*-完备   总被引:1,自引:0,他引:1  
杜妮 《数学研究》2007,40(1):86-89
首次给出有限群极大子群的强θ^*-完备的定义,利用这一概念得到关于群可解性、超可解性的新的充要条件.  相似文献   

11.
The discrete series characters of the finite general linear group GL(n, q) are expressed as uniquely defined integral linear combinations of characters induced from linear characters on certain subgroups Hd, n of GL(n, q). The coefficients in these linear combinations are determined (for all n, q) by a family of polynomials r(T) Z[T] indexed by the set of all partitions .  相似文献   

12.
In this paper, we characterize the dynamic of every Abelian subgroups of , or . We show that there exists a -invariant, dense open set U in saturated by minimal orbits with a union of at most n -invariant vector subspaces of of dimension n−1 or n−2 over . As a consequence, has height at most n and in particular it admits a minimal set in . This work is supported by the research unit: systèmes dynamiques et combinatoire: 99UR15-15  相似文献   

13.
Of interest are the subgroups of various groups which have nonempty intersection with each class of conjugate elements of the group under study. We call these subgroups conjugately dense and study Neumann's problem of describing them in the Chevalley groups over a field. The main theorem lists all conjugately dense subgroups of the Chevalley groups of Lie rank 1 over a locally finite field.  相似文献   

14.
We look at the structure of a soluble group G depending on the value of a function m(G)= max m p G), where m p(G)=max{logp|G:M| | M< G, |G:M|=p a}, p (G). Theorem 1 states that for a soluble group G, (1) r(G/ (G))= m(G); (2) d(G/ (G)) 1+ (m(G)) 3+m(G); (3) l p(G) 1+t, where 2t-1<m p(G) 2t. Here, (G) is the Frattini subgroup of G, and r(G), d(G), and l p(G) are, respectively, the principal rank, the derived length, and the p-length of G. The maximum of derived lengths of completely reducible soluble subgroups of a general linear group GL(n,F) of degree n, where F is a field, is denoted by (n). The function m(G) allows us to establish the existence of a new class of conjugate subgroups in soluble groups. Namely, Theorem 2 maintains that for any natural k, every soluble group G contains a subgroup K possessing the following properties: (1) m(K); k; (2) if T and H are subgroups of G such that K T <max <max H G then |H:T|=p t for some prime p and for t>k. Moreover, every two subgroups of G enjoying (1) and (2) are mutually conjugate.  相似文献   

15.
For any saturated formation F of finite groups containing all supersolvable groups, the groups in F are characterized by F-abnormal maximal subgroups.  相似文献   

16.
In this article we study locally nilpotent subgroups of D*: = GL 1(D), where D is a division ring. It is proved that every locally nilpotent subnormal subgroup of D* is central. If D is algebraic over its centre then every locally solvable subnormal subgroup of D* is central. Also, in this case, it is shown that every locally nilpotent maximal subgroup of D* can occur as the multiplicative group of some maximal subfield of D.  相似文献   

17.
n-极大子群为C-正规的有限群   总被引:3,自引:0,他引:3       下载免费PDF全文
首先,利用Hall子群的C-正规性,得到了有限群成为。可解群的一个充分条付,推广了Schur-Zassenhaus定理;其次,考查了 n-极大子群或其 2阶及 4阶循环子群为 C-正规对有限群结构的影响.  相似文献   

18.
Let D be an infinite division ring. A famous result due to Herstein says that every noncentral element of D has infinitely many conjugates in D. So, if D* is an FC-group, then D is a field. Now let N be a subnormal subgroup of GL n (D), where n ≥ 1, and M a maximal subgroup of N. In this article, we prove that if M is an FC-group, then M is contained in the multiplicative group of some subfield of M n (D).  相似文献   

19.
刘合国  马玉杰 《数学学报》2007,50(4):721-728
从自同构群的角度出发,给出了一些具有有限性条件的、最大Abel商群为局部循环群的可解群的结构.  相似文献   

20.
证明了非幂零极大子群共轭类类数等于2的有限群必可解,并给出了非幂零极大子群同阶类类数等于2的非可解群的等价刻画.  相似文献   

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