共查询到18条相似文献,搜索用时 265 毫秒
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作为之前工作的继续, 本文研究了无限亚局部循环群的结构以及它们的自同构和自同构群. 设 A,B 分别是秩1 的无挠Abel 群, G 为n 阶循环群. 群E 是A 被G 的扩张, G 被A 的扩张或者A 被 B 的扩张. 讨论了群E 的结构以及它们的自同构, 并得到了它们的自同构群. 相似文献
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有限ATI-群的类保持Coleman自同构 总被引:3,自引:3,他引:0
设G是一个有限群,对G的任意阿贝尔子群A及任意g∈G,若A∩A~g=1或A,则称G为一个ATI-群.本文证明了,对任意p∈τ(G),如果ATI-群G的一个p-方幂阶类保持自同构在G的任意Sylow子群上的限制等于G的某个内自同构的限制,则它必定是一个内自同构.作为该结果的一个直接推论,我们也证明了有限ATI-群G有正规化性质. 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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本文研究了有限群G的Coleman外自同构群是p'-群这个问题. 利用Sylow p-子群和同调群的性质,得到了有限群的Coleman外自同构群是p'-群的一些充分条件,其结果与M.Hertweck和W.Kimmerle得到的结果是不同的. 相似文献
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设G是无限Cernikov p-群,且G的每个真商群是Abel群,但G不是Abel群,本文确定了G的自同构群. 相似文献
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有限交涣p群的自同构群的阶的几点注记 总被引:1,自引:0,他引:1
本文用有限交换 P 群的自同构的阶的公式,讨论了有限交换 P 群及其自同构群的阶的关系,并证明各型 P~n 阶交换群适当排列以后,其自同构群的阶依次整除。由此推广了[2]、[3]中的相应结果。以下均设 G 是 P~n 阶交换群。G 的型为 相似文献
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《Indagationes Mathematicae (Proceedings)》1986,89(2):213-228
A lattice automorphism of a group is defined to be an automorphism of its lattice of subgroups. For a large class of finite simple Chevalley groups, it is shown that every lattice automorphism is induced by a group automorphism. However, this does not hold for all finite simple Chevalley groups G, as is shown by explicit construction in the case G=PSL(3, q). 相似文献
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Coleman Automorphisms of Extensions of Finite Characteristically Simple Groups by Some Finite Groups
Let G be an extension of a finite characteristically simple group by an abelian group or a finite simple group.It is shown that every Coleman automorphism of G is an inner automorphism.Interest in such automorphisms arises from the study of the normalizer problem for integral group rings. 相似文献
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设$G$是一个本原群,证明了存在某个素数$p$使得$G$的每个$p$-中心自同构是内自同构. 作为应用,证明了$G$的全形的每个Coleman自同构均为内自同构. 特别地,正规化子性质对对所讨论的这些群都成立. 另外也得到了其他一些相关结果. 相似文献
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Let G be a finite group. A Cayley graph over G is a simple graph whose automorphism group has a regular subgroup isomorphic to G. A Cayley graph is called a CI-graph(Cayley isomorphism) if its isomorphic images are induced by automorphisms of G. A well-known result of Babai states that a Cayley graph Γ of G is a CI-graph if and only if all regular subgroups of Aut(Γ) isomorphic to G are conjugate in Aut(Γ). A semi-Cayley graph(also called bi-Cayley graph by some authors) over G is a simple graph whose automorphism group has a semiregular subgroup isomorphic to G with two orbits(of equal size). In this paper, we introduce the concept of SCI-graph(semi-Cayley isomorphism)and prove a Babai type theorem for semi-Cayley graphs. We prove that every semi-Cayley graph of a finite group G is an SCI-graph if and only if G is cyclic of order 3. Also, we study the isomorphism problem of a special class of semi-Cayley graphs. 相似文献
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The Normalizer Property for Integral Group Rings of Holomorphs of Finite Groups with Trivial Center
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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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Let G be a basic classical Lie superalgebra except A(n, n) and D(2, 1, α) over the complex number field C. Using existence of a non-degenerate invariant bilinear form and root space decomposition, we prove that every 2-local automorphism on G is an automorphism. Furthermore, we give an example of a 2-local automorphism which is not an automorphism on a subalgebra of Lie superalgebra spl(3, 3). 相似文献
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The Wielandt subgroup of a group G,denoted by w(G),is the intersection of the normalizers of all subnormal subgroups of G.In this paper,the authors show that for a p-group of maximal class G,either wi(G) = ζi(G) for all integer i or wi(G) = ζi+1(G) for every integer i,and w(G/K) = ζ(G/K) for every normal subgroup K in G with K = 1.Meanwhile,a necessary and suflcient condition for a regular p-group of maximal class satisfying w(G) = ζ2(G) is given.Finally,the authors prove that the power automorphism group PAut(G) is an elementary abelian p-group if G is a non-abelian pgroup with elementary ζ(G) ∩ 1(G). 相似文献
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Gerhard Behrendt 《Order》1995,12(4):405-411
It is shown that a finite groupG is isomorphic to the automorphism group of a two-dimensional ordered set if and only if it is a generalized wreath product of symmetric groups over an ordered index set that is a dual tree. Furthermore, every finite abelian group is isomorphic to the full automorphism group of a three-dimensional ordered set. Also every finite group is isomorphic to the automorphism group of an ordered set that does not contain an induced crown with more than four elements. 相似文献