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1.
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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特征标表中零点个数很少的有限可解群 总被引:3,自引:1,他引:2
(1)与(2)均曾研究过有某特征标恰在两个共轭类上取非零值的有限群。本文讨论上述情形的另一极端,即每个不可约特征标至多在p个共轭类上取零值的有限可解群,这里p为群阶的最小素因子,通过对极小非交换商群的分析,我们将刻划这类群的结构。 相似文献
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非幂零极大子群指数为素数幂的有限群 总被引:7,自引:0,他引:7
郭秀云 《数学年刊A辑(中文版)》1994,(6)
本文证明了如下结果,1.设p是一个素数,如果有限群G的每一非幂零的极大子群的指数都为p的方幂,则G为可解群.2.如果有限群G的每一非幂零的极大子群的指数为素数幂,则G/S(G)1或PSL(2,7),其中S(G)表示G的最大可解正规子群. 相似文献
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共轭类的长和有限群的结构 总被引:4,自引:1,他引:3
设G是有限群,并设Con(G)是由G的一切共轭类组成的集合。本文目的是考察Con(G)的算术结构对G的群结构的影响。我们着重于Con(G)的p-部分结构,并得到关于p-幂零群的两个定理。这里,p表示一个有限群的最小素因子。用这两个定理,我们还得到若干结果,其中两个改进了D.Chillag和M.Herzog关于共轭类长的两个结果。 相似文献
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本文给出了有限交换局部环R上无限线性群GL(R)=∪nGLnR的Sylowp-了群的形式。令M是有限交换局部环R的唯一极大理想,k=R/M为R的剩余类域。用x(k)表示k的特征,并假定p与x(k)互素。 相似文献
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Curran第三猜想的一个反例 总被引:1,自引:1,他引:0
本文证明了:当p>2,n≥6时,存在p ̄n阶群G使得|AutG|=p ̄(n+1).由此得到3-群作为有限群的自同构群的最小阶为3 ̄7.从而给出了Gurran在1989年提出的猜想的一个反例。 相似文献
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设H是有限生成的无挠幂零群G的一个子群,如果H满足条件:对G的任意元素g及任意自然数n,从gn∈H可以推出g∈H,那么当素数p充分大时,∩∞i=1HGpi=H。 相似文献
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设p为奇素数,本文将用一些新的技巧来证明,当P是阶小于P^11的交换P-群时,自同构群方程Aut(X)=P无解。这个结果使MachHale在1983年的工作得到了突破,并且我们所给的方法具有广泛性。 相似文献
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Droste Manfred; Giraudet Michele; Gobel Rudiger 《Journal London Mathematical Society》2001,64(3):565-575
It is shown that each group is the outer automorphism groupof a simple group. Surprisingly, the proof is mainly based onthe theory of ordered or relational structures and their symmetrygroups. By a recent result of Droste and Shelah, any group isthe outer automorphism group Out (Aut T) of the automorphismgroup Aut T of a doubly homogeneous chain (T, ). However, AutT is never simple. Following recent investigations on automorphismgroups of circles, it is possible to turn (T, ) into a circleC such that Out (Aut T) Out (Aut C). The unavoidable normalsubgroups in Aut T evaporate in Aut C, which is now simple,and the result follows. 相似文献
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Yves de Cornulier 《代数通讯》2013,41(7):2337-2345
We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recently initiated by Bergman. Our main result is that G I is strongly bounded when G is a finite, perfect group and I is any set. This strengthens a result of Koppelberg and Tits. We also prove that ω1-existentially closed groups are strongly bounded. 相似文献
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We provide a sufficient condition for the nontriviality of the Lipschitz homotopy group of the Heisenberg group, ${\pi_m^{\rm Lip}(\mathbb{H}_n)}$ , in terms of properties of the classical homotopy group of the sphere, ${\pi_m(\mathbb{S}^n)}$ . As an application we provide a new simplified proof of the fact that ${\pi_n^{\rm Lip}(\mathbb{H}_n)\neq \{0\}, n=1,2,\ldots}$ , and we prove a new result that ${\pi_{4n-1}^{\rm Lip}(\mathbb{H}_{2n})\neq \{0\}}$ for n = 1,2,… The last result is based on a new generalization of the Hopf invariant. We also prove that Lipschitz mappings are not dense in the Sobolev space ${W^{1,p}(\mathcal{M},\mathbb{H}_{2n})}$ when ${\dim \mathcal{M} \geq 4n}$ and 4n?1 ≤ p < 4n. 相似文献
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We give a necessary and sufficient condition for two Hopf algebras presented as central extensions to be isomorphic, in a
suitable setting. We then study the question of isomorphism between the Hopf algebras constructed in [AG] as quantum subgroups
of quantum groups at roots of 1. Finally, we apply the first general result to show the existence of infinitely many non-isomorphic
Hopf algebras of the same dimension, presented as extensions of finite quantum groups by finite groups.
Partially supported by CONICET, ANPCyT, Secyt (UNC) and Ministerio de Ciencia y Tecnología de la Provincia de Córdoba. 相似文献
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Peter J. Cameron 《Journal of Algebraic Combinatorics》1996,5(4):315-322
A finite permutation group is cycle-closed if it contains all the cycles of all of its elements. It is shown by elementary
means that the cycle-closed groups are precisely the direct products of symmetric groups and cyclic groups of prime order.
Moreover, from any group, a cycle-closed group is reached in at most three steps, a step consisting of adding all cycles of
all group elements. For infinite groups, there are several possible generalisations. Some analogues of the finite result are
proved. 相似文献
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S. I. Adyan 《Mathematical Notes》2008,83(3-4):293-300
In the paper, the solvability of the word problem and the conjugacy problem is proved for a wide class of finitely presented groups defined by periodic defining relations of a sufficiently large odd degree. In the proof, we use a certain simplified version of the classification of periodic words and transformations of these words, which was presented in detail in the author’s monograph devoted to the well-known Burnside problem. The result is completed by the proof of an interesting result of Sarkisyan on the existence of a group, given by defining relations of the form E i 2 = 1, for which the word problem is unsolvable. This result was first published in abstracts of papers of the 13th All-Union Algebra Symposium in Gomel in 1975. 相似文献
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Over a commutative ring R with identity, free modules M with 2 distinguished submodules are studied. The category Rep2R of such objects M have the obvious morphisms between them, which are homomorphisms between .R-modules preserving the distinguished submodules. The endo-morphisms for each M constitute a subalgebra EndRM of the algebra EndRM and the readability of λ-generated R-algebras A as EndRM is considered for cardinals λ. Despite the fact that 4 is the minimal number of distinguished submodules for realizing any algebra over a field il, we are able to prove a similar result in Rep2R for many rings R including R = Z and algebras which are cotorsion-free. Several examples illustrate the boarder line of our main result. The main theorem is applied for constructing Butler groups in [11] 相似文献
20.
Groups of binary relations 总被引:5,自引:0,他引:5
It was shown in [3] that every finite group is the maximal subgroup of a semigroupB
x of all binary relations on some finite set X. This result is extended here to arbitrary groups. 相似文献