THE HOLOMORPHIC AUTOMORPHISM GROUP OF HIGHER DIMENSION THULLEN DOMAIN

In this paper, we give the holomorphic automorphism group of the higher-dimensional generalization of Thullen domain.

THE AUTOMORPHISM GROUP OF A LINEAR CODE

We know that for a code C,it‘s very important to find out the Automorphism groupAutC of C.However,it is very difficult to seek entire AutC.In this paper,using the G.I of matrices over a finite field,we give several methods to judge whether a permutation σ∈S_n.(Symmetric group) belongs to AutC or not.They are helpful for the purpose to ex-

The Automorphism Group of U（4,Z）

In this paper,the automorphism group of G is determined,where G is a 4 × 4 upper unitriangular matrix group over Z.Let K be the subgroup of AutG consisting of all elements of AutG which act trivially on G/G,G /ζG and ζG,then (i) InnG ■ K ■ AutG;(ii) AutG/K≌=G_1×D_8×Z_2,where G_1=(a,b,c|a^4=b^2=c^2=1,a^b=a^(-1),[a,c]= [b,c]=1 ;(iii) K/Inn G≌=Z×Z×Z.

Orders of Automorphism Groups of Some p-Groups

The orders of automorphism groups of the groups of order p^6 in the twelve family Ф12 axe produced, where p is an odd prime. Every group is analysed by utilizing the properties of metabelian, regularity and p-commutativity of finite p-groups, and the structure of the generators of its automorphism groups is obtained. Then the orders of automorphism groups are determined through some properties of equivalence in number theory.

FINITE GROUPS WHOSE AUTOMORPHISM GROUP HAS ORDER CUBEFREE

LetGdenote a finite group.It is shown that if|Aut(G)|is cubefree thenGpossesses the Sylow tower property.

Automorphism group of Green ring of Sweedler Hopf algebra

Let H2 be Sweedler＇s 4-dimensional Hopf algebra and r（H2） be the corresponding Green ring of H2. In this paper, we investigate the automorphism groups of Green ring r（H2） and Green algebra F（H2） = r（H2） zF, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r（H2） is isomorphic to K4, where K4 is the Klein group, and the automorphism group of F（H2） is the semidirect product of Z2 and G, where G = F ／ {1/2} with multiplication given by a. b = 1 - a - b ＋ 2ab.

Derivation algebra and automorphism group of generalized topological N = 2 superconformal algebra

We determine the derivation algebra and the automorphism group of the generalized topological N = 2 superconformal algebra.

Automorphism Group and Representation of a Twisted Multi-loop Algebra

Let G be the complexification of the real Lie algebra so（3） and A = C[t1^±1, t2^±1] be the Lau-ent polynomial algebra with commuting variables. Let L：（t1, t2, 1） = G c .A be the twisted multi-loop Lie algebra. Recently we have studied the universal central extension, derivations and its vertex operator representations. In the present paper we study the automorphism group and bosonic representations ofL（t1, t2, 1）.

Derivations and Automorphism Group of Original Deformative Schrodinger-Virasoro Algebra

In this paper, we determine the derivation algebra and the automorphism group of the original deformative Schrodinger-Virasoro algebra, which is the semi-direct product Lie algebra of the Witt algebra and its tensor density module Ig（a, b）.

Characterization of automorphism groups of sporadic simple groups

It is proved that all automorphism groups of the sporadic simple groups are characterized by their element orders and the group orders.

On the Characterizability of the Automorphism Groups of Sporadic Simple Groups by Their Element Orders

For G a finite group,π_e(G)denotes the set of orders of elements in G.If Ω is a subset of the set of natural numbers,h(Ω)stands for the number of isomorphism classes of finite groups with the same set Ω of element orders.We say that G is k-distinguishable if h(π_(G))=k<∞,otherwise G is called non-distinguishable.Usually,a 1-distinguishable group is called a characterizable group.It is shown that if M is a sporadic simple group different from M_(12),M_(22),J_2,He,Suz,M^cL and O'N, then Aut(M)is charaeterizable by its dement orders.It is also proved that if M is isomorphic to M_(12),M_(22),He,Suz or O'N,then h(π_e(Aut(M)))∈{1,∞}.

Finite Groups with Its Power Automorphism Groups Having Small Indices

In this paper, a finite group G with IAut（G） ： P（G）I ^- p or pq is determined, where P（G） is the power automorphism group of G, and p, q are distinct primes. Especially, we prove that a finite group G satisfies ｜Aut（G） ： P（G）｜= pq if and only if Aut（G）/P（G） ≌S3. Also, some other classes of finite groups are investigated and classified, which are necessary for the proof of our main results.

Graded Automorphism Group of TKK Lie Algebra over Semilattice

Every extended affine Lie algebra of type A1 and nullity v with extended affine root system R（A1, S）, where S is a semilattice in Rv, can be constructed from a TKK Lie algebra T（J（S）） which is obtained from the Jordan algebra ,：7（S） by the so-called Tits-Kantor-Koecher construction. In this article we consider the Zn-graded automorphism group of the TKK Lie algebra T（J（S））, where S is the ＂smallest＂ semilattice in Euclidean space Rn.

Finite Groups with Automorphism Groups Having Orders 4pq2 （2 〈 p 〈 q） II

The authors study and classify finite groups with their automorphism groups having orders 4pq2, where p and q axe primes such that 2 〈 p 〈 q. In 2013 the first and the third authors classified the nilpotent groups of this kind; here the authors give the classification of those finite non-nilpotent groups with their automorphism groups having orders 4pq2.

A Class of Pseudo-Real Riemann Surfaces with Diagonal Automorphism Group

A Riemann surface S having field of moduli M,but not a field of definition,is called pseudo-real.This means that S has anticonformal automorphisms,but none of them is an involution.A Riemann surface is said to be plane if it can be described by a smooth plane model of some degree d≥4 in P^2/C.We characterize pseudo-real-plane Riemann surfaces»S,whose conformal automorphism group Aut+(S)is PGL3(C)-conjugate to a finite non-trivial group that leaves invariant infinitely many points of P^2/C.In particular,we show that such pseudo-real-plane Riemann surfaces exist only if Aut+(S)is cyclic of even order n dividing the degree d.Explicit families of pseudo-reai-plane Riemann surfaces are given for any degree d=2pm with m>1 odd,p prime and n=d/p.

Periodicities in Cluster Algebras and Cluster Automorphism Groups

We study the relations between two groups related to cluster automorphism groups which are defined by Assem,Schiffler and Shamchenko.We establish the relation-ships among(strict)direct cluster automorphism groups and those groups consisting of periodicities of labeled seeds and exchange matrices,respectively,in the language of short exact sequences.As an application,we characterize automorphism-finite cluster algebras in the cases of bipartite seeds or finite mutation type.Finally,we study the relation between the group Aut(A)for a cluster algebra A and the group AutMn(S)for a mutation group Mn and a labeled mutation class S,and we give a negative answer via counter-examples to King and Pressland's problem.

Characterization of convex domains in C^2 with non-compact automorphism group

In the field of several complex variables, the Greene-Krantz Conjecture, whose consequences would be far reaching, has yet to be proven. The conjecture is as follows: Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} ? Aut(D) such that {gj(z)} accumulates at a boundary point p ∈ ?D for some z ∈ D. Then ?D is of finite type at p. In this paper, we prove the following result, yielding further evidence to the probable veracity of this important conjecture: Let D be a bounded convex domain in C^2 with C^2 boundary.Suppose that there is a sequence {gj} ? Aut(D) such that {gj(z)} accumulates at a boundary point for some point z ∈ D. Then if p ∈ ?D is such an orbit accumulation point, ?D contains no non-trivial analytic variety passing through p.

The Spectrum and Automorphism Group of the Set-Inclusion Graph

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 κ-and l-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).

Automorphism Groups of a Class of Cubic Cayley Graphs on Symmetric Groups

Let Sn denote the symmetric group of degree n with n 〉 3, S = {cn = （1 2…n）, cn^-1, （1 2）} and Fn=Cay（Sn, S） be the Cayley graph on Sn with respect to S. In this paper, we show that Fn （n 〉 13） is a normal Cayley graph, and that the full automorphism group of Fn is equal to Aut（Гn） = R（Sn） （Inn（C））≌- Sn×Z2, where R（Sn） is the right regular representation of Sn,φ = （1 2）（3 n）（4 n-1）（5 n-2）... （∈ Sn）, and Inn（C） is the inner isomorphism of Sn induced by φ .

The Automorphism Group of a Class of Nilpotent Groups with Infinite Cyclic Derived Subgroups

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 E-group E and a free abelian group A with rank m, where E={{1 kα1 kα2…kαn aα＋1 0 1 0 … 0 αn＋2 0 0 0 … 1 α2n＋1 0 0 0 …0 1}}αi∈Z,i=1,2,…,2n＋1},where k is a positive integer. Let AutG＇G be the normal subgroup of AutG consisting of all elements of AutG which act trivially on the derived subgroup G＇ of G, and Autc G/ζG,ζGG be the normal subgroup of AutG consisting of all central automorphisms of G which also act trivially on the center ζG of G. Then （i） The extension →AutG＇G→AutG→AutG＇→1 is split.（ii）AutG＇G/AutG/ζG,ζGG≈Sp（2n,Z）×（GL（m,Z）×（Z）m）,（iii）Aut GζG,ζGG/InnG≈（Zk）2n＋（Z）2nm.