共查询到19条相似文献,搜索用时 46 毫秒
1.
2.
3.
4.
5.
有限群为超可解群的充要条件 总被引:1,自引:0,他引:1
用置换条件刻画有限可解群的超可解性已有大量结果,本文的目的是给出另外一些有限可解群为超可解的充要条件。其主要结果是: 1.设G是满足置换条件的有限可解群,则G是超可解群当且仅当如下条件之一成立。 1)G的2-Sylow子群G_2的换位子群G_2′G. 2)G有正规2-补。 2.设G是有限可解群,则G超可解当且仅当G和G′均满足置换条件. 相似文献
6.
关于具有限秩的可解群 总被引:4,自引:0,他引:4
关于具有限秩的可解群本文得到了它的正规列的交换商因子的一种排序,推出了这类群的所有拟循环了群构成它的一个特征子群,了秩n的可解群的Hirsch不变量≤n,并由此界定了秩n的无挠可解群的导出长度。 相似文献
7.
本文证明了下面主要结果:设G是n-可解群,π是一些素数之集,若对任意p∈∩π(G),(p,n(1-n))=1,则G的π-Hall子群的个数r=k1k2...kt,每ki≡1(modp),某P∈π,且每ki整除G的一个主因子。 相似文献
8.
关于允许一个无不动点自同构群的有限群的可解性 总被引:1,自引:0,他引:1
关于允许一个无不动点自同构(群)的有限群的可解性的猜想是有限群研究中的一个重要问题。结果比较丰富的是限制该自同构群为一个p-群的情形。Thompson于1959年证明了p阶群的情形。Martineail于1971年证明了初等Abel p-群的情形。Rickman于1979年证明了p2阶群的情形。本文借助Glauberman的一个定理,对p=2或3的一般情形给出了肯定的回答。实际上是用较初等的方法证明了更为广泛一些的结论。 相似文献
9.
设G是个有限可解解,若对G的每个商群H,H的正规Abel子群都是可以由2元生成的,则称G为AD2-群,在本文里,我们证明了:如果G是个AD2-群,那么G是3元生定的,且G^(6)=1。另外,我们举了2个例子,说明这些界都是最好的。 相似文献
10.
超可解群的若干充分条件 总被引:12,自引:1,他引:11
关于有限超可解的研究已有不少结果,本文在苏向盈研究有限群的半正规子群的基础上又得到了一系列新的结果(文中定理2—9),本文还对[1]中定理6的证明进行了改进并得到了重要推论,改进的方法在本文得到了充分应用.文中所说群均为有限群,使用的符号是规范的. 相似文献
11.
The arguments of Cannon, Floyd, Grayson and Thurston (Geom. Dedicata (1989), 291–300) showing that solvegeometry groups are not almost convex apply to solvable Baumslag-Solitar groups. 相似文献
12.
Given an arbitrary identity v=1, there exists a positive integer N=N(v) such that for every metabelian group G and every generating set A for G the following holds: If each subgroup of G generated by at most N elements of A satisfies the identity v=1 then the group G itself satisfies this identity. A similar assertion fails for center-by-metabelian groups. This answers Bludov's question. 相似文献
13.
14.
Shi Rong LI 《数学学报(英文版)》2005,21(4):797-802
For a finite group G, let T(G) denote a set of primes such that a prime p belongs to T(G) if and only if p is a divisor of the index of some maximal subgroup of G. It is proved that if G satisfies any one of the following conditions: (1) G has a p-complement for each p∈T(G); (2)│T(G)│= 2: (3) the normalizer of a Sylow p-subgroup of G has prime power index for each odd prime p∈T(G); then G either is solvable or G/Sol(G)≌PSL(2, 7) where Sol(G) is the largest solvable normal subgroup of G. 相似文献
15.
We consider solvable invariant subgroups of a finite group with bounded primary indices of maximal subgroups. We establish that an invariant subgroup of this type belongs to the product of classical formations and investigate its dispersibility. 相似文献
16.
We study solvable groups of infinite special rank all proper normal subgroups of which define quotient groups of finite special rank. 相似文献
17.
Risto Atanasov 《代数通讯》2013,41(6):2130-2139
A subgroup H of a group G is a solitary subgroup of G if G does not contain another isomorphic copy of H. Combining together the concepts of solitary subgroups and solvable groups, we define (normal) solitary solvable groups and (normal) strongly solitary solvable groups. We derive several results that hold for these groups and we discuss classes of groups that, under certain hypotheses, are (normal) solitary solvable and (normal) strongly solitary solvable. We also derive several results about p-groups that are solitary solvable. 相似文献
18.
《代数通讯》2013,41(7):3287-3293
Abstract For an element a of a group G,let S(a) denote the semigroup generated by all conjugates of a in G. We prove that if G is solvable of finite rank and 1 ? S(a) for all 1 ≠ a ∈ G,then ?a G ?/?b G ? is a periodic group for every b ∈ S(a). Conversely if every two generator subgroup of a finitely generated torsion-free solvable group G has this property then G has finite rank,and if every finitely generated subgroup has this property then every partial order on G can be extended to a total order. 相似文献
19.