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automorphism Groups of Some Finite Groups

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Science China Mathematics 1994年第3期37卷 295-303页

作者：李世荣 Department of Mathematics Guangxi University.Naming 530004PRC

Let G be a group of odd order In this paper we prove that G cannot function as the full automorphism group of a finite group when G has a small order.

关键词： finite group automorphism group order

automorphism Groups of Bouwer Graphs

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Algebra Colloquium 2018年第3期25卷 493-508页

作者： Mimi Zhang Jinxin Zhou Department of Mathematics Beijing Jiaotong University Beijing 100044 China

Let k, m and n be three positive integers such that 2^m= 1 （mod n） and k ≥ 2. The Bouwer graph, which is denoted by B（k,m,n）, is the graph with vertex set {（a,b）｜ a ∈Zm, b ∈Zn×…×Zn} k-1 times and two vertices being adjacent if they can be written as （a,b） and （a＋ 1,c）, where either c ： b or c = （cl,c2 …,ck-1） differs from b = （b1, b2,…, bk-1） in exactly one position, say the jth position, where cj = bj ＋ 2^a. Every B（k, m, n） is a vertex- and edge-transitive graph, and Bouwer proved that B（k, 6, 9） is half-arc-transitive for every k ≥ 2. In 2016, Conder and Zitnik gave the classification of half-arc-transitive Bouwer graphs. In this paper, the full automorphism group of every B（k, m, n） is determined.

关键词： Bouwer graph Cayley graph automorphism half-arc-transitive

automorphism groups of some algebras

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Science China Mathematics 2009年第2期52卷 323-328页

作者： PARK Hong Goo LEE Jeongsig CHOI Seul Hee NAM Ki-Bong Department of Mathematics Hanyang UniversitySeoul 133-791 Korea Department of General Studies and Education SamYuk University Cheongnyangi P.O.Box 118Seoul 130-650 Korea Department of Mathematics University of JeonjuChon-ju 560-759 Korea Department of Mathematics and Computer Sciences University of Wisconsin-WhitewaterWhitewater WI53190 USA

The automorphism groups of algebras are found in many papers. Using auto-invariance, we find the automorphism groups of the Laurent extension of the polynomial ring and the quantum n-plane (respectively, twisting polynomial ring) in this work. As an application of the results of this work, we can find the automorphism group of a twisting algebra. We define a generalized Weyl algebra and show that the generalized Weyl algebra is simple. We also find the automorphism group of a generalized Weyl algebra. We show that the generalized Weyl algebra Am,m+n is the universal enveloping algebra of the generalized Witt algebra W(m,m + n).

关键词： Laurent extension quantum n-plane (generalized) Weyl algebra automorphism auto-invariant 17B40 17B56

automorphism group on the Toeplitz algebras

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Chinese Science Bulletin 1996年第8期41卷 617-620页

作者：严从荃孙顺华 Department of Mathematics Sichuan Union University Chengdu 610064 China

Let B be the unit ball of Cn, S2n-1 the unit sphere of Cn. The concept of the Toeplitzoperators on Hardy space H2(S2n-1) is as usual. Denote by C(S2n-1) the algebra of all con-tinuous functions on S2n-1, and (C(S2n-1)... 详细信息

关键词： Toeplitz algebras automorphism group extensions of C*-algebras several complex variables.

automorphism GROUP OF 2-D DE BRUIJN-GOOD GRAPH

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Chinese Science Bulletin 1991年第4期36卷 270-274页

作者：刘木兰 Institute of Systems Science Academia Sinica Beijing 100080 PRC

Let m, n be positive integers, M an arbitrary set. The de Bruijn-Good Graph over M of dimension 2 and order (m, n) is the digraph with vertex set V consisting of all m×n matrices over M, i. e.

关键词： automorphism group 2-D de Bruijn-Good Graph.

On automorphism groups of some finite groups

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Science China Mathematics 2003年第4期46卷 450-458页

作者：钱国华 Department of Mathematics Suzhou University Suzhou 215006China Department of Mathematics ChangShu CollegeChangshu 215500China

We show that if n＞1 is odd and has no divisor p4 for any prime p, then there is no finite group G such that |Aut(G)| = n.

关键词： finite group, automorphism of group, group construction.

Explicit formula of holomorphic automorphism group on complex homogeneous bounded domains

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Science China Mathematics 2006年第10期49卷 1392-1404页

作者： XU Yichao,CHEN Minru & MA Songya Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China College of Mathematics and Information Sciences, Henan University, Kaifeng 475001, China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China College of Mathematics and Information Sciences Henan University Kaifeng China

We known that the maximal connected holomorphic automorphism group Aut (D)(0) is a semi-direct product of the triangle group T(D) and the maximal connected isotropic subgroup Iso (D)(0) of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(VN,F).In this paper, we give the explicit formula of any holomorphic automorphism in T(D(VN,F)) and Iso (D(VN, F))(0), where G(0) is the unit connected component of the Lie group G.

关键词： holomorphic automorphism group, homogeneous Siegel domain, normal Siegel domain, complex homogeneous bounded domain.

A result about Abelian automorphism groups

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Science China Mathematics 1997年第5期40卷 494-500页

作者：班桂宁俞曙霞 Department of Mathematics Guangxi University Nanning 530004 China

Some new techniques are given to prove that two sorts of Abelian groups cannot function as the full automorphism groups of the finite groups. With generality these techniques made a breakthrough in MacHale’s problem.

关键词： finite group p-group automorphism Abelian group defining relation.

Full automorphism group of the generalized symplectic graph

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Science China Mathematics 2013年第7期56卷 1509-1520页

作者： ZENG LiWei CHAI Zhao FENG RongQuan MA ChangLi LMAM School of Mathematical Sciences Peking University Science China Press College of Mathematics and Information Science Hebei Normal University

Let Fq be a finite field of odd characteristic, m, v the integers with 1 ≤ m ≤ v and K a 2v × 2v nonsingular alternate matrix over Fq. In this paper, the generalized symplectic graph GSp2v（q, m） relative to K over Fq is introduced. It is the graph with m-dimensional totally isotropic subspaces of the 2v-dimensional symplectic space Fq（2v） as its vertices and two vertices P and Q are adjacent if and only if the rank of PKQw is 1 and the dimension of P ∩ Q is m - 1. It is proved that the full automorphism group of the graph GSp2v（q, m） is the projective semilinear symplectic group P∑p（2v, q）.

关键词： generalized symplectic graph automorphism projective generalized symplectic group totally isotropic subspace generalized dual polar graph