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1.
给出了带极大或极小条件的Abel群A的自同构群以及自同态环的相伴Lie环是可解或幂零的充要条件.同时也给出了群A=Q_(π1)⊕Q_(π2)⊕…⊕Q_(πr)的自同构群是可解或幂零的充要条件,以及群A的自同态环的相伴Lie环是可解或幂零的充要条件. 相似文献
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令G是一个奇阶群。本文证明了:当G具有小阶时,G不能作为一个有限群的全自同构群。 相似文献
5.
证明了: 若n是大于1的奇数, 使得对任意素数p都有p4æn, 则不存在有限群G, 使得|Aut(G)| = n. 相似文献
6.
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
7.
本文利用一种新方法,考虑交换群Cp2×Cp 的自同构群,得到了该自同构群的结构.我们的结论是:Aut(Cp2×Cp)[Cp- 1∝(Cp×Cp)]holCp. 相似文献
8.
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
9.
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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O. S. Maslakova 《Algebra and Logic》2003,42(4):237-265
It is proved that the fixed point group of an arbitrary automorphism of a free group of finite rank has an algorithmically computable basis. 相似文献
12.
The Automorphism Tower of a Free Group 总被引:2,自引:0,他引:2
It is proved that the automorphism group of any non-abelianfree group F is complete. The key technical step in the proofis that the set of all conjugations by powers of primitive elementsis first-order parameter-free definable in the group Aut(F). 相似文献
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Let φ be an automorphism of a free group Fn of rank n, and let Mφ = Fn ?φ ? be the corresponding mapping torus of φ. We study the group Out(Mφ) under certain technical conditions on φ. Moreover, in the case of rank 2, we classify the cases when this group is finite or virtually cyclic, depending on the conjugacy class of the image of φ in GL2(?). As an application, we solve the isomorphism problem for the family of F2-by-? groups, in terms of the two defining automorphisms. 相似文献
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V. G. Bardakov 《Algebra and Logic》2003,42(5):287-303
We examine the automorphism group Aut(F
n
) of a free group F
n
of rank n 2 on free generators x
1, x
2,...,x
n
. It is known that Aut(F
2) can be built from cyclic subgroups using a free and semidirect product. A question remains open as to whether this result can be extended to the case n > 2. Every automorphism of Aut(F
n
) sending a generator x
i
to an element f
i
-1
x
(i)
f
i
, where f
i
F
n
and is some permutation on a symmetric group S
n
, is called a conjugating automorphism. The conjugating automorphism group is denoted C
n
. A set of automorphisms for which is the identity permutation form a basis-conjugating automorphism group, denoted Cb
n
. It is proved that Cb
n
can be factored into a semidirect product of some groups. As a consequence we obtain a normal form for words in C
n
. For n 4, C
n
and Cb
n
have an undecidable occurrence problem in finitely generated subgroups. It is also shown that C
n
, n 2, is generated by at most four elements, and we find its respective genetic code, and that Cb
n
, n 2, has no proper verbal subgroups of finite width. 相似文献
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确定了广义超特殊p-群G的自同构群的结构.设|G|=p~(2n+m),|■G|=p~m,其中n≥1,m≥2,Aut_fG是AutG中平凡地作用在Frat G上的元素形成的正规子群,则(1)当G的幂指数是p~m时,(i)如果p是奇素数,那么AutG/AutfG≌Z_((p-1)p~(m-2)),并且AutfG/InnG≌Sp(2n,p)×Zp.(ii)如果p=2,那么AutG=Aut_fG(若m=2)或者AutG/AutfG≌Z_(2~(m-3))×Z_2(若m≥3),并且AutfG/InnG≌Sp(2n,2)×Z_2.(2)当G的幂指数是p~(m+1)时,(i)如果p是奇素数,那么AutG=〈θ〉■Aut_fG,其中θ的阶是(p-1)p~(m-1),且Aut_f G/Inn G≌K■Sp(2n-2,p),其中K是p~(2n-1)阶超特殊p-群.(ii)如果p=2,那么AutG=〈θ_1,θ_2〉■Aut_fG,其中〈θ_1,θ_2〉=〈θ_1〉×〈θ_2〉≌Z_(2~(m-2))×Z_2,并且Aut_fG/Inn G≌K×Sp(2n-2,2),其中K是2~(2n-1)阶初等Abel 2-群.特别地,当n=1时... 相似文献
17.
Referring to Tits alternative, we develop a necessary and sufficient condition to decide whether the normalizer of a finite group of integral matrices is polycyclic-by-finite or is containing a non-Abelian free group. This result is of fundamental importance to conclude whether the (outer) automorphism group of a Bieberbach group is polycyclic-by-finite or has a non-cyclic free subgroup. 相似文献
18.
确定了超特殊Z-群的自同构群.设G是超特殊Z-群,即G={(1 α_1 α_2···α_n α_(n+1) 0 1 0···0 α_(n+2) ···0 0 0 ··· 0 α_2n 0 0 0··· 1 α_(2n+1) 0 0 0···1 α_(2n+1) 0 0 0···0 1)|α_j∈Z,j=1,2,3,...,2n+1}Aut_cG是AutG中平凡作用在ζG上的自同构形成的正规子群,则AutG=Aut_cG×Z_2,且1→Z···Z}2N→Aut_cG→Sp(2n,Z)→1是正合列. 相似文献
19.
Let F
n
be the free group on n ≥ 2 elements and Aut(F
n
) its group of automorphisms. In this paper we present a rich collection of linear representations of Aut(F
n
) arising through the action of finite-index subgroups of it on relation modules of finite quotient groups of F
n
. We show (under certain conditions) that the images of our representations are arithmetic groups.
Received: November 2006, Accepted: March 2007 相似文献