The Automorphism Group of the Lie Group T（D（V_N,F））

In this paper,the authors determine maximal connected automorphism group of the Lie transformation group T（D（VN,F））,which acting on the normal Siegel domain D（VN,F）is simple and transitive,and prove that the maximal connected automorphism group of T（D（VN,F））is its maximal connected inner automorphism group.     

The complete classification of Steiner systems S(2, 4, 25)

We describe an algorithm that was used to classify completely all Steiner systems S(2, 4, 25). The result is that in addition to the 16 nonisomorphic designs with nontrivial automorphism group already known, there are precisely two such nonisomorphic designs with a trivial automorphism group. © 1996 John Wiley & Sons, Inc.     

Automorphism groups of pictures

A picture is a simple graph together with an edge-coloring, such that each vertex is incident with exactly one edge of each color. An automorphism of a picture is a graph automorphism that preserves the colors of the edges. We show that every group is isomorphic to the full automorphism group of a picture, and prove that a group is isomorphic to a vertex-transitive subgroup of the automorphism group of a picture if and only if it can be generated by involutions.     

Cluster automorphism groups of cluster algebras with coefficients

We study the cluster automorphism group of a skew-symmetric cluster algebra with geometric coefficients. We introduce the notion of gluing free cluster algebra, and show that under a weak condition the cluster automorphism group of a gluing free cluster algebra is a subgroup of the cluster automorphism group of its principal part cluster algebra (i.e., the corresponding cluster algebra without coefficients). We show that several classes of cluster algebras with coefficients are gluing free, for example, cluster algebras with principal coefficients, cluster algebras with universal geometric coefficients, and cluster algebras from surfaces (except a 4-gon) with coefficients from boundaries. Moreover, except four kinds of surfaces, the cluster automorphism group of a cluster algebra from a surface with coefficients from boundaries is isomorphic to the cluster automorphism group of its principal part cluster algebra; for a cluster algebra with principal coefficients, its cluster automorphism group is isomorphic to the automorphism group of its initial quiver.     

Flag-transitive 2- $$(v,k,\lambda )$$ ( v,k , λ ) designs with $$r>\lambda (k-3)$$ r > λ ( k - 3 )

Designs, Codes and Cryptography - In this paper, we study the flag-transitive automorphism groups of 2-designs and prove that if G is a flag-transitive automorphism group of a 2-design $$\mathcal...     

Automorphisms of quasitriangular algebras

The outer automorphism group of a nest algebra is canonically isomorphic to the (spatial) automorphism group of the nest itself. The outer automorphism group of the associated quasitriangular algebra is canonically isomorphic to a group of “approximate” automorphisms of the nest. A simple proof that every derivation of a quasitriangular algebra is inner is obtained as a corollary.     

On a theorem of Burnside on fixed-point-free automorphisms

We prove that a finite group having a fixed-point-free automorphism in the Fitting subgroup of its automorphism group must be abelian of rather restricted structure. As a consequence, no finite nonabelian group could have a fixed-point-free automorphism in the Frattini subgroup of its automorphism group. Received: 21 April 2007, Revised: 18 May 2007     

A complete classification of symmetric (31, 10, 3) designs

In recent years several authors have determined all symmetric (31, 10, 3) designs with a nontrivial automorphism. Here we describe an algorithm for the generation by computer of all symmetric (31, 10, 3) designs and find that there are precisely 151 such nonisomorphic designs. Of these, 107 have a trivial automorphism group.     

An Embedding Theorem for Automorphism Groups of Cartan Geometries

We study the automorphism group of a Cartan geometry, and prove an embedding theorem analogous to a result of Zimmer for automorphism groups of G-structures. Our embedding theorem leads to general upper bounds on the real rank or nilpotence degree of a Lie subgroup of the automorphism group. We prove that if the maximal real rank is attained in the automorphism group of a geometry of parabolic type, then the geometry is flat and complete.     

Automorphism group and dimension of ordered sets

It is shown that a finite groupG is isomorphic to the automorphism group of a two-dimensional ordered set if and only if it is a generalized wreath product of symmetric groups over an ordered index set that is a dual tree. Furthermore, every finite abelian group is isomorphic to the full automorphism group of a three-dimensional ordered set. Also every finite group is isomorphic to the automorphism group of an ordered set that does not contain an induced crown with more than four elements.     

On the residual finiteness of outer automorphisms of relatively hyperbolic groups

We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable relatively hyperbolic group is residually finite. As a direct consequence, we obtain that the outer automorphism group of a limit group is residually finite.     

Factor group of the automorphism group of a matroid basis graph with respect to the automorphism group of the matroid

Any automorphism of a matroid induces an automorphism of its basis graph. We try to determine what can be said concerning the automorphisms of the basis graph which are not induced by matroids' automorphisms. In particular, we determine the structure of the factor group of the automorphism group of the basis graph with respect to the automorphism group of the matroid, in the event that this factor group exists.     

On the lattice automorphisms of the finite Chevalley groups

A lattice automorphism of a group is defined to be an automorphism of its lattice of subgroups. For a large class of finite simple Chevalley groups, it is shown that every lattice automorphism is induced by a group automorphism. However, this does not hold for all finite simple Chevalley groups G, as is shown by explicit construction in the case G=PSL(3, q).     

Twisted conjugacy classes of the unit element

We study twisted conjugacy classes of the unit element in different groups. Fel’shtyn and Troitsky showed that the twisted conjugacy class of the unit element of an abelian group is a subgroup for every automorphism. The structure is investigated of a group whose twisted conjugacy class of the unit element is a subgroup for every automorphism (inner automorphism).     

Isomorphisms of adjoint Chevalley groups over integral domains

It is shown that every automorphism of an adjoint Chevalley group over an integral domain containing the rational number field is uniquely expressible as the product of a ring automorphism, a graph automorphism and an inner automorphism while every isomorphism between simple adjoint Chevalley groups can be expressed uniquely as the product of a ring isomorphism, a graph isomorphism and an inner automorphism. The isomorphisms between the elementary subgroups are also found having analogous expressions.

     

Coleman自同构群的投射极限

在这篇注记中，利用群的投射极限性质给出了有限可解群的Coleman自同构群的一个具体构造.作为应用，证明了二面体群的Coleman外自同构群或者是1或者是一个初等阿贝尔2-群.     

Coleman自同构群的投射极限

在这篇注记中,利用群的投射极限性质给出了有限可解群的Coleman自同构群的一个具体构造.作为应用,证明了二面体群的Coleman外自同构群或者是1或者是一个初等阿贝尔2-群.     

素特征域上广义Witt李超代数的自同构群

设W是素特征域上无限维或有限维广义Witt李超代数.本文利用W的自然滤过不变性和W的底代数的不变维数性质,证明了W的自同构群AutW同构于W的底代数的容许自同构群,还证明了在此群同构之下,AutW的标准正规列恰好对应W的底代数的容许自同构群的标准正规列,并给出AutW若干较为细致的性质.     

Coleman Automorphisms of Extensions of Finite Characteristically Simple Groups by Some Finite Groups

Let G be an extension of a finite characteristically simple group by an abelian group or a finite simple group.It is shown that every Coleman automorphism of G is an inner automorphism.Interest in such automorphisms arises from the study of the normalizer problem for integral group rings.