拟极小外p-自同构不动点子群为p阶的p-群

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.     

可除阿贝尔p-群的自同构群

主要探讨了秩大于或者等于p-1的可除阿贝尔p-群的p-自同构群,并且得到这些p-自同构如何作用在该可除阿贝尔p-群上.这些结论有助于进一步理解Cernikov p-群的结构.     

一类无限Cernikov p-群的自同构群北大核心CSCD

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.     

有限秩的幂零p-群的p-自同构

设G是一个有限秩的幂零p-群,α和β是G的两个p-自同构,记I= ((αβ(g))(βα(g))-1)|g∈G),则(i)当I是有限循环群时,α和β生成一个有限P-群; (ii)当I是拟循环p-群时,α和β生成一个可解的剩余有限P-群,它是有限生成的无挠幂零群被有限p-群的扩张．     

关于广义超特殊p-群的自同构群

用如下的方式确定了广义超特殊p-群G的自同构群.设|G|=p2n+m,|ζG|=pm,|N|=pl并且G'≤N≤ζG,其中n≥1且m≥2.AutnG表示AutG中平凡地作用在N上的所有自同构形成的正规子群.则(1)当p是奇素数时,AutG/AunG≌Z(p-1)pl-1.进一步地,(i)如果G的幂指数是pm,则Autn...     

一类p''''-自由的幂零群的p-自同构(Ⅱ)

设G=KP,其中K是有限生成的p'-自由的幂零群,P是有限秩的幂零p-群,并且[K,P]=1,即G是K和P的中心积,α和β是G的两个p-自同构,记I=〈(αβ(g))·(βα(g))-1|g∈G〉,则(i)当I=Zpn (○+) Zp∞时,α和β生成一个可解的剩余有限p-群,它是有限生成的无挠幂零群被有限p-群的扩张;在下列3种情形下,α和β生成一个可解的剩余有限p-群,其幂零长度不超过3.(ii)当I=Z (○+) Zp∞时;(iii)当I有正规列1＜J＜I,其商因子分别为无限循环群和有限循环群时;(iv)当I有正规列1＜L＜J＜I,其3个商因子分别为无限循环群、有限循环群和拟循环p-群时.特别地,当上述群K是一个FC-群时,α和β生成的群是有限生成的无挠幂零群被有限p-群的扩张.     

一类中心循环的有限p-群的自同构群的研究

本文研究了一类中心循环的有限p-群G的自同构群.利用在G的导群上作用平凡的自同构以及环上的辛群和正交群,确定了G的自同构群的结构,这推广了Bornand的相应结果.     

一类p′-自由的幂零群的p-自同构(Ⅱ)

设G=KP,其中K是有限生成的p′-自由的幂零群,P是有限秩的幂零p-群,并且[K,P]=1,即G是K和P的中心积,α和β是G的两个p-自同构,记I:=〈(αβ(g))·(βα(g))~(-1)|g∈G〉,则(i)当I=Z_(p~n)(?)Z_(p~∞)时,α和β生成一个可解的剩余有限p-群,它是有限生成的无挠幂零群被有限p-群的扩张;在下列3种情形下,α和β生成一个可解的剩余有限p-群,其幂零长度不超过3.(ii)当I=Z(?)Z_(p~∞)时;(iii)当I有正规列1相似文献   

广义超特殊p-群的自同构群(Ⅱ)

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.     

无限正则p-群

对一类无限正则p-群进行了研究,得到了一个正则的局部幂零p-群G如果满足|G(Ω)1(G)|＜∞,那么G是幂零的且G是可除阿贝尔p-群被有限群的扩张.进而,还研究了一类无限的非正则p-群,但它的所有真商群或者真的无限子群是正则群.在假设这类群存在拟循环子群的情况下,在定理1.2和1.3给出了这类群的结构的刻画.     

On noninner automorphisms of 2-generator finite p-groups

A longstanding conjecture asserts that every finite nonabelian p-group admits a noninner automorphism of order p. In this paper we give some necessary conditions for a possible counterexample G to this conjecture, in the case when G is a 2-generator finite p-group. Then we show that every 2-generator finite p-group with abelian Frattini subgroup has a noninner automorphism of order p.     

On the Existence of a Noninner Automorphism of Order p for p-Groups

We obtain sufficient conditions for the existence of a noninner automorphism of order p for finite p-groups. We show that groups of order p ⁿ (n < 7, p is a prime number, p > 3) possess a noninner automorphism of order p.     

具有一个T．I．Sylow 2-子群的有限群的类保持Coleman自同构

设G是一个有限群,它的Sylow 2-子群是T.I.集,证明了如果G的2的方幂阶类保持自同构在G任意的Sylow子群上的限制等于G的某个内自同构的限制,则它一定是一个内自同构.对这样的自同构的研究是由整群环的同构问题所引起的.     

2-Local Automorphisms on Basic Classical Lie Superalgebras

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).     

本原群的p-中心自同构及其应用

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.     

二极大子群为TI-子群的有限群的类保持Coleman自同构

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.     

CLASSIFICATION OF A CLASS OF HYPERBOLIC REINHARDT DOMAINS

In this article, the author discusses the dimension of holomorphic automorphism groups on hyperbolic Reirihardt domains. and classifies those hyperbolic Reinhardt domains whose automorphism group has prescribed dimension n2 - 2 (where n is the dimension of domain).     

Weakly power automorphisms of groups

An automorphism α of a group G is called a weakly power automorphism if it maps every non-periodic subgroup of G onto itself. The aim of this paper is to investigate the behavior of weakly power automorphisms. In particular, among other results, it is proved that all weakly power automorphisms of a soluble non-periodic group G of derived length at most 3 are power automorphisms, i.e. they fix all subgroups of G. This result is best possible, as there exists a soluble non-periodic group of derived length 4 admitting a weakly power automorphism, which is not a power automorphism.     

Automorphisms of Tensor Completions of Algebras

In the classical representation of different groups, frequent use is made of a linear automorphism group of various algebras. Since the linear automorphism group is only part of a full automorphism group, such an approach might seem to be too restrictive. In this connection, we point out a natural, wide class of algebras whose automorphisms are standard and are reducible to linear. Thus, for algebras in this class, studying the full automorphism group reduces to treating the linear, a traditional approach in the class of such algebras being quite general.__________Translated from Algebra i Logika, Vol. 44, No. 3, pp. 368–382, May–June, 2005.