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1.
s-半置换子群对有限群的p-超可解性的影响 总被引:1,自引:0,他引:1
群G的子群H称为半置换的,若对任意的K≤G,只要(|H|,|K|)=1,就有HK=KH.H称为s-半置换的,若对任意的p||G|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G).本文研究Sylow子群的极大子群及极小子群的s-半置换性对有限群的p-超可解性的影响. 相似文献
2.
群G的子群H称为半置换的,若对任意的K≤G,只要(|H|,|K|)=1.就有HK=KH,H称为s-半置换的,若对任意的p‖G|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G).本文利用Sylow子群的2-极大子群的s-半置换性得到有限群为p-幂零群的一些充分条件. 相似文献
3.
对于有限群G的极大子群M,令β(G:M)表示整除│G:M│的素因子个数,β(G)表示所有β(G;M)中的最大数.令μ(G)为使得β(G:M)=β(G)的极大子群的集合.通过对这一类极大子群的θ-偶赋予一定条件,得到了判断群G可解、超可解的新结果. 相似文献
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5.
设G为有限群,称G的子群H为ss-置换子群,如果存在G的次正规子群B使得G=HB,且H与B的任意Sylow子群可以交换,即对任意X∈Syl(B)有XH=HX.利用子群的ss-置换性来研究有限群的结构,得到有限群超可解的两个充分条件. 相似文献
6.
半正规n-极大子群对有限群结构的影响 总被引:1,自引:0,他引:1
设△↓n(G)为有限群G的n次极大子群的全体。1.若△↓4(G)中的子群均在G中半正规,则下述结论之一成立:(1)G是可解群;(2)G/φ(G)=A5,(3)G/φ(G)=PSL(2,13);(4)G/φ(G)=PSL(2,p),满足p=4p1 1=6p2-1,这里p1≥43,p2≥29;(5)G/φ(G)=PSL(2,p),满足p=6p1 1=4p2-1,这里p1≥7,p2≥11.2。2.设3不属于π(G),若△↓(G)中的子群均在G中半正规,则G是可解群,或G/φ(G)=Sz(2^3). 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.
二次极大子群中2阶及4阶循环子群拟中心的有限群 总被引:1,自引:0,他引:1
本文讨论2阶及4阶循环子群对群结构的影响.证明二次极大子群中2阶及4阶循环子群拟中心的有限群G同构于下列群之一:(1)G为2-闭群;(2)G为2-幂零群;(3)G≌S,;(4)G=PQ.其中P为2^4阶广义四元数群,Q≌C3;(5)G≌A5或SL(2,5). 相似文献
9.
群G的子群H称为G的等中心化子群(简称为G的EC子群),如果H的非单位元素在G内的中心化子都相等. 等中心化子群的问题与有限几何的研究有联系.王萼芳教授在文[1]中完全决定了对称群及交错群的全部等中心化子群. 本文主要是提出了一种方法来确定有限群的等中心化子群,然后运用此方法给出了对称群及交错群的等中心化子群的另一求法,并且求出了一些射影特殊线性群的全部等中心化子群. 相似文献
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11.
Ali Reza Ashrafi 《Algebra Colloquium》2000,7(2):139-146
For a finite group G, let Cent(G) denote the set of centralizers of single elements of G and #Cent(G) = |Cent(G)|. G is called an n-centralizer group if #Cent(G) = n, and a primitive n-centralizer group if #Cent(G) = #Cent(G/Z(G)) = n. In this paper, we compute #Cent(G) for some finite groups G and prove that, for any positive integer n 2, 3, there exists a finite group G with #Cent(G) = n, which is a question raised by Belcastro and Sherman [2]. We investigate the structure of finite groups G with #Cent(G) = 6 and prove that, if G is a primitive 6-centralizer group, then G/Z(G) A4, the alternating group on four letters. Also, we prove that, if G/Z(G) A4, then #Cent(G) = 6 or 8, and construct a group G with G/Z(G) A4 and #Cent(G) = 8.This research was in part supported by a grant from IPM.2000 Mathematics Subject Classification: 20D99, 20E07 相似文献
12.
For a finite groupG, #Cent(G) denotes the number of centralizers of its elements. A groupG is calledn-centralizer if #Cent(G) =n, and primitive n-centralizer if $\# Cent(G) = \# Cent\left( {\frac{G}{{Z(G)}}} \right) = n$ . The first author in [1], characterized the primitive 6-centralizer finite groups. In this paper we continue this problem and characterize the primitive 7-centralizer finite groups. We prove that a finite groupG is primitive 7-centralizer if and only if $\frac{G}{{Z(G)}} \cong D_{10} $ orR, whereR is the semidirect product of a cyclic group of order 5 by a cyclic group of order 4 acting faithfully. Also, we compute#Cent(G) for some finite groups, using the structure ofG modulu its center. 相似文献
13.
LetG be a finite group and #Cent(G) denote the number of centralizers of its elements.G is calledn-centralizer if #Cent(G)=n, and primitiven-centralizer if #Cent(G)=#Cent(G/Z(G))=n. In this paper we investigate the structure of finite groups with at most 21 element centralizers. We prove that such a group is solvable and ifG is a finite group such thatG/Z(G)?A5, then #Cent(G)=22 or 32. Moroever, we prove that A5 is the only finite simple group with 22 centralizers. Therefore we obtain a characterization of A5 in terms of the number of centralizers 相似文献
14.
Ali Reza Ashrafi 《Journal of Applied Mathematics and Computing》2000,7(1):115-124
For a finite groupG, #Cent(G) denotes the number of centralizers of its elements. A groupG is called n-centralizer if #Cent(G) =n, and primitiven-centralizer if # Cent(G)\text = # Cent\text(\fracGZ(G))\text = n\# Cent(G){\text{ = \# }}Cent{\text{(}}\frac{G}{{Z(G)}}){\text{ = }}n. In this paper we compute the number of distinct centralizers of some finite groups and investigate the structure of finite groups with exactly six distinct centralizers. We prove that ifG is a 6-centralizer group then % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% WGhbaabaGaamOwaiaacIcacaWGhbGaaiykaaaacaqGGaGaeyyrIaKa% aeiiaGqaciaa-readaWgaaWcbaGaa8hoaaqabaGccaGGSaGaaeiiai% aa-feadaWgaaWcbaGaa8hnaaqabaGccaGGSaGaaeiiaiaabQfadaWg% aaWcbaGaaeOmaaqabaGccaqGGaGaey41aqRaaeiiaiaabQfadaWgaa% WcbaGaaeOmaaqabaGccaqGGaGaey41aqRaaeiiaiaabQfadaWgaaWc% baGaaeOmaaqabaGccaqGGaGaae4BaiaabkhacaqGGaGaaeOwamaaBa% aaleaacaqGYaaabeaakiaabccacqGHxdaTcaqGGaGaaeOwamaaBaaa% leaacaqGYaaabeaakiaabccacqGHxdaTcaqGGaGaaeOwamaaBaaale% aacaqGYaaabeaakiaabccacqGHxdaTcaqGGaGaaeOwamaaBaaaleaa% caqGYaaabeaaaaa!62C4!\[\frac{G}{{Z(G)}}{\text{ }} \cong {\text{ }}D_8 ,{\text{ }}A_4 ,{\text{ Z}}_{\text{2}} {\text{ }} \times {\text{ Z}}_{\text{2}} {\text{ }} \times {\text{ Z}}_{\text{2}} {\text{ or Z}}_{\text{2}} {\text{ }} \times {\text{ Z}}_{\text{2}} {\text{ }} \times {\text{ Z}}_{\text{2}} {\text{ }} \times {\text{ Z}}_{\text{2}} \] . 相似文献
15.
HUANG WEN-LIN 《数学研究通讯:英文版》2018,(2):106-116
In this paper,we define a group Tp(G) of p-endotrivial kG-modules and a generalized Dade group Dp(G) for a finite group G.We prove that Tp(G) ≌ Tp(H) whenever the subgroup H contains a normalizer of a Sylow p-subgroup of G,in this case,K(G) ≌ K(H).We also prove that the group Dp(G) can be embedded into Tp(G) as a subgroup. 相似文献
16.
本文首先将Hal定理推广为:设N为G的正规子群,若N为Enπ群,G/N为Dπ群,则G为Dπ群.在此基础上得到了群G为Enπ群的充要条件为:(1)G存在正规子群N,满足N及G/N为Enπ群;(2)对任意p∈π,任意q∈π {p}及任意p 元素x,CG(x)含G的Sylowq 子群.另外,我们对非Able单群的情形也进行了一些讨论. 相似文献
17.
设G为一个torsion-free的离散群,(G,G+)为一个拟序群,记T^G (G)为相应的Toeplitz算子代数,K(l^2(G 1)为l^2(G )上的紧算子全体,本文证明了K(l^2(G ))增包含于T^G (G)当且仅当下列两个条件时满足。(1)(G,G+)为一个序群,(2)G中存在一个最小的正元。 相似文献
18.
Let G be a group and πe(G) the set of element orders of G.Let k∈πe(G) and m k be the number of elements of order k in G.Letτe(G)={mk|k∈πe(G)}.In this paper,we prove that L2(16) is recognizable byτe (L2(16)).In other words,we prove that if G is a group such that τe(G)=τe(L2(16))={1,255,272,544,1088,1920},then G is isomorphic to L2(16). 相似文献
19.
V. Uma 《Transformation Groups》2007,12(2):371-406
In this paper we describe the G × G-equivariant K-ring of X, where X is a regular compactification of a connected complex
reductive algebraic group G. Furthermore, in the case when G is a semisimple group of adjoint
type, and X its wonderful compactification, we describe its ordinary K-ring K(X). More precisely, we prove that K(X) is a
free module over K(G/B) of rank the cardinality of the Weyl group. We further give an explicit basis of K(X) over K(G/B),
and also determine the structure constants with respect to this basis. 相似文献
20.
Let G be a finite group, Irr(G) denotes the set of irreducible complex characters of G and gG the conjugacy class of G containing element g. A well-known theorem of Burnside([1,Theorem 3.15]) states that every nonlinear X ∈ Irr(G) has a zero on G, that is, an element x (or a conjugacy class xG) of G with X(x) = 0. So, if the number of zeros of character table is very small, we may expect, the structure of group is heavily restricted. For example, [2, Proposition 2.7] claimes that G is a Frobenius group with a complement of order 2 if each row in charcter table has at most one zero (its proof uses the classification of simple groups). In this note, we characterize the finite group G satisfying the following hypothesis: 相似文献