共查询到20条相似文献,搜索用时 15 毫秒
1.
Henry Wilton 《Geometric And Functional Analysis》2008,18(1):271-303
A celebrated theorem of Marshall Hall Jr. implies that finitely generated free groups are subgroup separable and that all
of their finitely generated subgroups are retracts of finite-index subgroups. We use topological techniques inspired by the
work of Stallings to prove that all limit groups share these two properties. This answers a question of Sela.
Received: May 2006 Revision: May 2007 Accepted: May 2007 相似文献
2.
与正规性相关的各种子群之间的关系 总被引:5,自引:0,他引:5
本讨论了正规子群,拟正规子群,s-拟正规子群,半正规子群,c-正规子群,次正规子群,共轭置换子群,半置换子群,s-半置换子群这九种子群之间的关系。 相似文献
3.
本文以根系及Weyl群为基础,以换位子公式为工具,对任意域上任意类型Chevalley群,针对极大抛物子群情形,确定了Levi子群在抛物子群中的所有扩群. 相似文献
4.
We give criteria to characterize subgroups of a direct product of finite solvable groups that satisfy the strong Frattini argument. 相似文献
5.
If G is a nonsoluble finite group, the intersection of the maximal subgroups of G which are not nilpotent is the Frattini subgroup of G. This was proved by Shidov (1971). The authors here present a new formation ? larger than the formation of the nilpotent groups for which the analogous of the theorem of Shidov holds. The theorem makes use of the classification of finite simple groups. 相似文献
6.
AbstractIn this paper, we introduce the concept of sse-embedded subgroups of finite groups and present some new characterizations of solubility of finite groups using the sse-embedding property of subgroups. Furthermore, we discuss the sse-embedded subgroups in finite nonabelian simple groups. Some previously known results are generalized and unified. 相似文献
7.
CHEN GuiYun & LI JinBao School of Mathematics Statistics Southwest University Chongqing China School of Mathematical Sciences Xuzhou Normal University Xuzhou China 《中国科学A辑(英文版)》2009,(2)
Let A be a subgroup of a group G and X be a nonempty subset of G. A is said to be X-semipermutable in G if A has a supplement T in G such that A is X-permutable with every subgroup of T. In this paper, we investigate further the influence of X-semipermutability of some subgroups on the structure of finite groups. Some new criteria for a group G to be supersoluble or p-nilpotent are obtained. 相似文献
8.
Following Rose, a subgroup H of a group G is called contranormal, if G = H G . In certain sense, contranormal subgroups are antipodes to subnormal subgroups. It is well known that a finite group is nilpotent if and only if it has no proper contranormal subgroups. However, for the infinite groups this criterion is not valid. There are examples of non-nilpotent infinite groups whose subgroups are subnormal; in paricular, these groups have no contranormal subgroups. Nevertheless, for some classes of infinite groups, the absence of contranormal subgroups implies the nilpotency of the group. The current article is devoted to the search of such classes. Some new criteria of nilpotency in certain classes of infinite groups have been established. 相似文献
9.
《代数通讯》2013,41(9):3225-3238
ABSTRACT A cover for a group G is a collection of proper subgroups whose union is the whole group G. A cover is irredundant if no proper sub-collection is also a cover, and is called maximal if all its members are maximal subgroups. For an integer n > 2, a cover with n members is called an n-cover. Also, we denote σ (G) = n if G has an n-cover and does not have any m-cover for each integer m < n. In this article, we completely characterize groups with a maximal irredundant 6-cover with core-free intersection. As an application of this result, we characterize the groups G with σ (G) = 6. The intersection of an irredundant n-cover is known to have index bounded by a function of n, though in general the precise bound is not known. We also prove that the exact bound is 36 when n is 6. 相似文献
10.
张志让 《数学年刊A辑(中文版)》2004,(2)
设G是任意群,群G的Frattini子群nat(G)定义为G的所有极大子群的交.类似地,群G的另外两个特征子群nFrat(G)及R(G)分别定义为群G的所有极大正规子群及群G的所有正规的极大子群的交.本文通过对nat(G),nnat(G)及R(G)的相互包含关系的研究,得到CF-群或中心由多重循环群的扩张群中局部幂零性的一个判定准则.同时也讨论了在某些群类中若干种广义幂零性的等价性. 相似文献
11.
Let G be a finite group. Fix a prime divisor p of IGI and a Sylow p-subgroup P of G, let d be the smallest generator number of P and Ma(P) denote a family of maximal subgroups P1, P2 , Pd of P satisfying ∩^di=1 Pi = Ф(P), the Frattini subgroup of P. In this paper, we shall investigate the influence of s-conditional permutability of the members of some fixed .Md(P) on the structure of finite groups. Some new results are obtained and some known results are generalized. 相似文献
12.
Guo和Chen在2010年引入了弱c-可置换子群的概念,并利用这种新的广义置换性质对有限群的结构给出了一些新的刻画.本文推广了上述文献中的两个主要结论,确定了极小子群为弱c-可置换子群的有限群的结构. 相似文献
13.
本文证明了非单群系列SL(2,q)(q=p ̄n>3)可以仅用其极大子群阶之集来刻划,从而得到了SL(2,q)的一个特征性质. 相似文献
14.
In this paper, we investigate the structure of the groups whose nontrivial normal subgroups have order two. Some properties of this kind of groups are obtained. 相似文献
15.
本文研究了非平凡正规子群的阶相同的有限群. 给出了非平凡正规子群唯一的可解群的结构. 对非可解群的情况, 我们也给出了它的刻画. 相似文献
16.
A subgroup H is called ?-supplemented in a finite group G, if there exists a subgroup B of G such that G = HB and H 1 B is a proper subgroup of G for any maximal subgroup H 1 of H. In this article, we investigate the influence of ?-supplementation of some primary subgroups in finite groups. Some new results about supersolvable groups and formation are obtained. 相似文献
17.
In this paper, we investigate the finite groups all of whose non-normal nilpotent subgroups are cyclic. We show that such groups are solvable with cyclic centers. If G is a non-supersolvable group, then G has only one non-cyclic Sylow subgroup which is either isomorphic to Q8 or is of type (q, q). 相似文献
18.
19.
W. Mack Hill 《Israel Journal of Mathematics》1977,26(1):68-74
In the context of the problem of which nonabelianp-groups can occur as normal subgroups contained in Frattini subgroups, the family of supernilpotent groups (all maximal subgroups characteristic) is investigated. Results of this investigation are applied to the Frattini-embedding problem, incorporating recent work of A. R. Makan. The groups of order 2n (n ≦ 6) have been examined with respect to supernilpotence and their occurrence as normal subgroups contained in Frattini subgroups. Results of this examination are presented. 相似文献