共查询到19条相似文献,搜索用时 78 毫秒
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确定了广义超特殊p-群G的自同构群的结构.假设|G|=p^2n+m,|ζG|=p^m,其中n≥1,m≥2,(1)当p是奇数时,记AutG'G={α∈AutG|α在G上作用平凡},则(i)AutG'G Aut G,Aut G/AutG'G=~Zp-1;(ii)如果G的幂指数是p^m,那么AutG'G/InnG=~Sp(2n,p)×Zp^m-1;(iii)如果G的幂指数是p^m+1,那么AutG'G/InnG=~(K×Sp(2n-2,p))×Zp^m-1,其中K是p^2n-1阶超特殊p-群.特别地,当n=1时,AutG'G/Inn G=~Zp×Zp^m-1.(2)当p=2时,(i)如果G的幂指数是2^m,那么Out G=~Sp(2n,2)×Z2×Z2^m-2.特别地,当n=1时,|Aut G|=3·2^m+2,Aut G的Sylow子群都不是正规子群,并且Aut G的Sylow 2-子群都同构于HK,其中H=Z2×Z2×Z2×Z2^m-2,K=Z2.(ii)如果G的幂指数是2^m+1,那么OutG=~(ISp(2n2,2))×Z2×Z2^m-2,其中I是一个2^2n-1阶初等Abel 2-群.特别地,当n=1时,|AutG|=2^m+2并且Aut G=~HK,其中H=Z2×Z2×Z2^m-1,K=Z2. 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|=p2n+m,|ζG|=pm,其中n≥1,m≥2,AutfG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pm时,(i)如果p是奇素数,那么Aut G/AutfG≌Z(p_1)pm-2,并且AutfG/Inn G≌Sp(2n,p)×zp.(ii)如果p=2,那么AutG=AutfG(若m=2)或者AutG/AutfG≌Z2m-3×z2(若m≥3),并且AutfG/InnG≌Sp(2n,2)× z2.(2)当G的幂指数是pm+1时,(i)如果p是奇素数,那么AutG=<θ>×AutfG,其中p的阶是(p-1)pm-1,且AutfG/InnG≌K(×)Sp(2n-2,p),其中K是p2n-1阶超特殊p-群.(ii)如果p=2,那么Aut G=<θ1,θ2>(×) AutfG,其中<θ1,θ2>=<θ1>×<θ2>≌Z2m-2×Z2,并且AutfG/InnG≌K(×)Sp(2n-2,2),其中K是22n-1阶初等Abel 2-群.特别地,当n=1时,AutfG/InnG≌Zp. 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
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重新确定了广义超特殊p-群G的自同构群的结构.设|G|=p~(2n+m),|ζG|=p~m,其中n≥1,m≥2,Aut_cG是AutG中平凡地作用在ζG上的元素形成的正规子群,则(i)若p是奇素数,则AutG=〈θ〉×Aut_cG,其中θ的阶是(p-1)p~(m-1);若p=2,则AutG=〈θ_1,θ_2〉×Aut_cG,其中〈θ_1,θ_2〉=〈θ_1〉×〈θ_2〉≌Z_(2m-2)×Z_2.(ii)如果G的幂指数是p~m,那么Aut_cG/InnG≌Sp(2n,p).(iii)如果G的幂指数是p~(m+1),那么Aut_cG/InnG≌K×Sp(2n-2,p),其中K是p~(2n-1)阶超特殊p-群(若p是奇素数)或者初等Abel 2-群.特别地,当n=1时,Aut_cG/InnG≌Z_p. 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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The Automorphism Group of a Class of Nilpotent Groups with Infinite Cyclic Derived Subgroups 下载免费PDF全文
The automorphism group of a class of nilpotent groups with infinite cyclic derived subgroups is determined. Let G be the direct product of a generalized extraspecial Z-group E and a free abelian group A with rank m, where E ={(1 kα_1 kα_2 ··· kα_nα_(n+1) 0 1 0 ··· 0 α_(n+2)...............000...1 α_(2n+1)000...01|αi∈ Z, i = 1, 2,..., 2 n + 1},where k is a positive integer. Let AutG G be the normal subgroup of Aut G consisting of all elements of Aut G which act trivially on the derived subgroup G of G, and AutG/ζ G,ζ GG be the normal subgroup of Aut G consisting of all central automorphisms of G which also act trivially on the center ζ G of G. Then(i) The extension 1→ Aut_(G') G→ AutG→ Aut(G')→ 1 is split.(ii) Aut_(G') G/Aut_(G/ζ G,ζ G)G≌Sp(2 n, Z) ×(GL(m, Z)■(Z~)m).(iii) Aut_(G/ζ G,ζ GG/Inn G)≌(Z_k)~(2n)⊕(Z)~(2nm). 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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In this paper we are interested in the automorphism group of the poset B
m, n
. B
m, n
constitutes the words obtained from the cyclic word of length n on an alphabet of m letters in by deleting on all possible ways and their natural order. We prove:
Résumé: Le but de ce papier est la détermination du groupe d"automorphismes des ordres B
m, n
. Il s"agit des mots obtenus à partir du mot cyclique de longeur n sur un alphabet de m lettres par suppression successive de lettres et ordonnés naturellement. On prouve: AutB
m, n
= {S
n
for 1 n m, S
2 S
2m-n
for m + 1n 2m - 1, S
2for 2m n. 相似文献
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Let n,k and l be integers with 1 ≤ k < l ≤ n-1.The set-inclusion graph G(n,k,l) is the graph whose vertex set consists of all k-andl-subsets of[n]={1,2,...,n},where two distinct vertices are adjacent if one of them is contained in the other.In this paper,we determine the spectrum and automorphism group of G(n,k,l). 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
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文献[1]从Euclid空间R^v(v≥1)的一个半格S出发,定义了一个Jordan代数J(S):然后通过Tits—Kantor-Koecher方法由J(S)构造出Lie代数G(J(S)).最后利用G(J(S))得到A1型扩张仿射Lie代数L(J(S)).本文给出v=2,S为格时。A1型扩张仿射Lie代数L(J(S))的Z^2一分次自同构群. 相似文献
18.
M. J. Curran 《代数通讯》2013,41(1):389-397
The article considers when the direct product of two finite groups has an Abelian automorphism group. 相似文献
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In this paper, the automorphism group of a generalized extraspecial p-group G is determined, where p is a prime number. Assume that |G| = p 2n+m and |ζG| = p m , where n 1 and m 2. (1) When p is odd, let Aut G G = {α∈ AutG | α acts trivially on G }. Then Aut G G⊿AutG and AutG/Aut G G≌Z p-1 . Furthermore, (i) If G is of exponent p m , then Aut G G/InnG≌Sp(2n, p) × Z p m-1 . (ii) If G is of exponent p m+1 , then Aut G G/InnG≌ (K Sp(2n-2, p))×Z p m-1 , where K is an extraspecial p-group of order p 2n-1 . In particular, Aut G G/InnG≌ Z p × Z p m-1 when n = 1. (2) When p = 2, then, (i) If G is of exponent 2 m , then AutG≌ Sp(2n, 2) × Z 2 × Z 2 m-2 . In particular, when n = 1, |AutG| = 3 · 2 m+2 . None of the Sylow subgroups of AutG is normal, and each of the Sylow 2-subgroups of AutG is isomorphic to H K, where H = Z 2 × Z 2 × Z 2 × Z 2 m-2 , K = Z 2 . (ii) If G is of exponent 2 m+1 , then AutG≌ (I Sp(2n-2, 2)) × Z 2 × Z 2 m-2 , where I is an elementary abelian 2-group of order 2 2n-1 . In particular, when n = 1, |AutG| = 2 m+2 and AutG≌ H K, where H = Z 2 × Z 2 × Z 2 m-1 , K = Z 2 . 相似文献