共查询到19条相似文献,搜索用时 109 毫秒
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设$H$是有限群$G$的一个子群,若对任意$g\in G$, $H\cap H^g=1$或者$H$,则称$H$为TI-子群. 设$G$是一个所有二极大子群为TI-子群的有限群,本文证明了$G$的每个类保持Coleman自同构是内自同构. 作为本结果的一个直接推论,得到了这样的群$G$有正规化子性质. 相似文献
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Mazur猜想:具有阿贝尔Sylow 2-子群的有限群有正规化子性质.设G是一个有限群,N是G的一个正规子群且Z(G/N)仅有平凡单位,本文建立了由Z(G/N)中单位诱导的G的自同构与N的Coleman自同构之间的联系,在此基础上证明了若G是一个具有阿贝尔Sylow 2-子群的有限群且Z(G/F*(G))仅有平凡单位,则Mazur猜想对G成立. 相似文献
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阶为某素数p的方幂的自同构如果不是内自同构,则称其为外p-自同构.如果φ是群G的外p-自同构且o(φ)=p,其中φ是φ在Out(G)=Aut(G)/Inn(G)中的自然同态像,则称φ为群G的拟极小外p-自同构.设φ是有限p-群G的任意拟极小外p-自同构,给出了|C_G(φ)|≤p时G的结构. 相似文献
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设群G为有限群,日为G的子群.若对任意的g∈G,日为〈H,H~g〉的Hall子群,则称子群日为G的Hall共轭嵌入子群.利用Hall共轭嵌入子群得到有限群G分别为幂零群与超可解群的若干新的判定方法. 相似文献
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一类不能作为自同构群的奇阶群 总被引:2,自引:0,他引:2
本文考虑如下问题:怎样的有限群可以作为另一个有限群的全自同构群?我们首先证明,若有限群K有一个正规Sylowp-子群使得|K:Z(K)|p=p2,那么K有2阶自同构.利用这个结果,我们证明了,若奇阶群G具有阶Psm(1≤s≤3),p为|G|的最小素因子,pm,m无立方因子,则G不可能作为全自同构群. 相似文献
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Martin Hertweck 《Monatshefte für Mathematik》2002,242(2):1-7
Let G be a finite group whose Sylow 2-subgroups are either cyclic, dihedral, or generalized quaternion. It is shown that a class-preserving automorphism of G of order a power of 2 whose restriction to any Sylow subgroup of G equals the restriction of some inner automorphism of G is necessarily an inner automorphism. Interest in such automorphisms arose from the study of the isomorphism problem for integral group rings, see [6, 7, 13, 14]. 相似文献
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The Normalizer Property for Integral Group Rings of Holomorphs of Finite Groups with Trivial Center 下载免费PDF全文
Let G=Hol(H) be the holomorph of a finite group H. If there is a prime q dividing |H| such that every q-central automorphism of H is inner and Z(H)=1, then every Coleman automorphism of G is inner. In particular, the normalizer property holds for G. 相似文献
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Martin Hertweck 《Monatshefte für Mathematik》2002,136(1):1-7
Let G be a finite group whose Sylow 2-subgroups are either cyclic, dihedral, or generalized quaternion. It is shown that a class-preserving
automorphism of G of order a power of 2 whose restriction to any Sylow subgroup of G equals the restriction of some inner automorphism of G is necessarily an inner automorphism. Interest in such automorphisms arose from the study of the isomorphism problem for
integral group rings, see [6, 7, 13, 14].
Received 30 September 2001; in revised form 10 December 2001 相似文献
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Let Mod(S) be the extended mapping class group of a surface S. For S the twice-punctured torus, we show that there exists an isomorphism of finite index subgroups of Mod(S) which is not the restriction of any inner automorphism. For S a torus with at least three punctures, we show that every injection of a finite index subgroup of Mod(S) into Mod(S) is the restriction of an inner automorphism of Mod(S); this completes a program begun by Irmak. We also establish the co-Hopf property for finite index subgroups of Mod(S).Dan Margalit: Partially supported by an NSF postdoctoral fellowship 相似文献
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A power automorphism θ of a group G is said to be pre-fixed-point-free if CG(θ) is an elementary abelian 2-group. G is called an E-group if G has a pre-fixed-point-free power automorphism. In this paper, finite E-groups, together with all their pre-fixed-point-free power automorphisms, are completely determined. Moreover, a characteristic of finite abelian groups is given, which explains some known facts concerning power automorphisms. 相似文献
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M. Shabani-Attar 《代数通讯》2013,41(6):2437-2442
Let G be a finite non-abelian p-group, where p is a prime. An automorphism α of G is called a class preserving automorphism if α(x) ∈ x G the conjugacy class of x in G, for all x ∈ G. An automorphism α of G is called an IA-automorphism if x ?1α(x) ∈ G′ for each x ∈ G. In this paper, we give necessary and sufficient conditions on finite p-group G of nilpotency class 2 such that every IA-automorphism is class preserving. 相似文献
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有限幂零群通过单群扩张的整群环的正规化子性质 总被引:1,自引:1,他引:0
设G是一个有限幂零群通过单群的扩张,即G有一个幂零正规子群N,使得G/N是单群.本文证明了这样的有限群G具有正规化子性质.特别地,内可解群有正规化子性质. 相似文献
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设G=A\×P是阿贝尔群$A$与极大类p -群P的半直积,其中P中的元以幂自同构的方式作用于A. 该文证明了G的每个Coleman自同构都是内自同构.作为该结果的一个直接推论, 作者得到了这样的群$G$有正规化子性质. 相似文献
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设G 是一个剩余有限的minimax 可解群, α 是G 的几乎正则自同构, 则G/[G, α] 是有限群, 并且(1) 当αp = 1 时, G 有一个指数有限的幂零群其幂零类不超过h(p), 其中h(p) 是只与素数p 有关的函数.(2) 当α2 = 1 时, G 有一个指数有限的Abel 特征子群且[G, α]′ 是有限群.关键词剩余有限minimax 可解群几乎正则自同构 相似文献