共查询到20条相似文献,搜索用时 15 毫秒
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In this paper, the normalizers of some classes of subgroups of the braid group B
n+1 are studied. 相似文献
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The work is inspired by an article of Herzog, Longobardi, and Maj, who considered groups with a finite number of infinite conjugacy classes. Their main results were obtained under assumption that the FC-center is of finite index in the group. We consider here infinite groups with a finite number of conjugacy classes of any size (FNCC-groups). Hence the FC-center in our case will be finite, but of infinite index in the group. Among results on these groups we give a criterion for a wreath product of FNCC-groups to be an FNCC-group. 相似文献
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N. M. Suchkov 《Acta Appl Math》2005,85(1-3):285-289
We present a short review of the recent results about infinite groups with given strongly insolated, strongly embedded subgroups and Zassenhaus groups.
This research is supported by Krasnoyarsk Science Foundation, grant 11F202C, the Russian Foundation for Basic Research, grant 03-01-00356.Mathematics Subject Classifications (2000) 20B07, 20B22. 相似文献
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P. Arroyo-Jordá 《代数通讯》2013,41(8):2923-2929
The main aim of this article is to obtain the characterization of local Schunck classes of finite groups whose projectors have the cover and avoidance property on Abelian chief factors. 相似文献
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Manoj K. Yadav 《代数通讯》2013,41(9):3350-3354
Let G be a finite group and M(G) be the subgroup of G generated by all noncentral elements of G that lie in the conjugacy classes of the smallest size. Recently several results have been proved regarding the nilpotency class of M(G) and F(M(G)), where F(M(G)) denotes the Fitting subgroup of M(G). We prove some conditional results regarding the nilpotency class of M(G). 相似文献
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A group G is said to have the Bergman property (the propertyof uniformity of finite width) if given any generating X withX = X1 of G, we have that G = Xk for some natural k,that is, every element of G is a product of at most k elementsof X. We prove that the automorphism group Aut(N) of any infinitelygenerated free nilpotent group N has the Bergman property. Also,we obtain a partial answer to a question posed by Bergman byestablishing that the automorphism group of a free group ofcountably infinite rank is a group of uniformly finite width. 相似文献
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We consider the graph Γ(G), associated with the conjugacy classes of a group G. Its vertices are the nontrivial conjugacy classes of G, and we join two different classes C, D, whenever there exist x ∈ G and y ∈ D such that xy = yx. The aim of this article is twofold. First, we investigate which graphs can occur in various contexts and second, given a graph Γ(G) associated with G, we investigate the possible structure of G. We proved that if G is a periodic solvable group, then Γ(G) has at most two components, each of diameter at most 9. If G is any locally finite group, then Γ(G) has at most 6 components, each of diameter at most 19. Finally, we investigated periodic groups G with Γ(G) satisfying one of the following properties: (i) no edges exist between noncentral conjugacy classes, and (ii) no edges exist between infinite conjugacy classes. In particular, we showed that the only nonabelian groups satisfying (i) are the three finite groups of order 6 and 8. 相似文献
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V. Tarieladze 《Journal of Mathematical Sciences》2014,197(6):858-861
A class $ \mathcal{G} $ of maximally almost periodic (MAP) topological Abelian groups is called a UMAP-class if it has the following property: if G is an Abelian group and τ 1 and τ 2 are distinct group topologies in G such that (G, τ 1) and (G, τ 2) are in $ \mathcal{G} $ , then (G, τ 1)∧ ≠ (G, τ 2)∧. Several examples of UMAP-classes are discussed. In particular, it is shown that the class PMAP of all Polish MAP-groups is a UMAP-class. 相似文献
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For an arbitrary variety
of groups and an arbitrary class
of groups that is closed on quotient groups, we prove that a quotient group G/N of the group G possesses an invariant system with
- and
-factors (respectively, is a residually
-group) if G possesses an invariant system with
- and
-factors (respectively, is a residually
-group) and N
(respectively, N is a maximal invariant
-subgroup of the group G). 相似文献
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Let
be a class of groups. The elementary class with base
is defined as the minimal class of groups containing
and closed with respect to taking subgroups, quotient groups, group extensions, and direct limits. Properties of such classes are studied. Some applications to the theory of elementary amenable groups and a relation to the Kurosh--Chernikov classes of generalized solvable groups are considered. 相似文献
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Xiaolei Liu 《代数通讯》2013,41(4):1443-1449
We extend the two results of Dolfi and Isaacs to π-separable groups, where π = {p, q}, from solvable groups. 相似文献
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Esther Beneish 《代数通讯》2013,41(12):4552-4566
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Let G be a finite group written multiplicatively and k a positive integer. If X is a non-empty subset of G, write X
2 = |xy | x, y X . We say that G has the small square property on k-sets if |X
2| < k
2 for any k-element subset X of G. For each group G, there is a unique m = m
G
such that G has the small square property on (m + 1)-sets but not on m-sets. In this paper we show that given any positive integer d, there is a finite group G with m
G
= d. 相似文献
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记ZG为有限群G的整群环,△n(G)为增广理想△(G)的n次幂,Qn(G)=△"(G)/△n 1(G)为G的增广商群.本文考虑了二面体群D2tk(k 奇)和m次对称群Sm,证明了Qn(D2tk)为秩不超过2t 1的基本2-群以及Qn(Sm)≌Z2. 相似文献