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一个地图的自同构就是到它本身的一个同构。An automorphism of a map is an isomorphism from the map to itself.

给出了这个非结合代数的自同构。The forms of any automorphism of the non-associative algebra are also given.

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一个图称为点传递图，如果它的全自同构群在它的顶点集合上作用传递。G is called point transitive if it has a point transitive automorphism group.

本文研究了一类非结合代数的自同构。In this paper, we study the automorphism of a type of non-associative algebra.

给出了一类新的试验多项式，可识别多项式代数的非线性自同构。We can distinguish nonlinear automorphism of polynomials algebra by using the test polynomials.

经常，两个或者更多的不同的几何有同构的自同构群。Quite often, it appears there are two or more distinct geometries with isomorphic automorphism groups.

群G的一个元素g称为G的检验元素，如果G的每一个保持g不变的自同态都是G的自同构。An element gis a test element of a group G if every homomorphism of G which keeps g fixed is an automorphism.

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最后确定了W及其泛中心扩张的自同构群的结构。Finally, the structures of the automorphism groups of W and its universal central extension are characterized.

在举一例，不同曲率半径的椭圆几何有同构的自同构群。To take another example, elliptic geometries with different radii of curvature have isomorphic automorphism groups.

第二章，主要研究有限反射群的最长元以及和最长元相对应的有限反射群的自同构。In Chapter 2, we investigate the longest elements and the corresponding special automorphism of finite reflection groups.

第二章应用拟群，直积自同构群及其他方法构作各图的带洞图设计。In Chapter 2, construct some holey H-designs using quasigroups, directed product automorphism group as well as other methods.

而把同样的性质应用到恒同自同构，我们会得到李群中有限阶共轭类的闭性定理。And if we apply the same property to the identity automorphism , we get the closedness theorem for conjugacy classes of finite order in Lie groups.

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具体地构造出两个有限循环群的自由积的外自同构群，并给出了其阶的计算公式。The outer automorphism group of the free product of two cyclic groups is constructed, and two exact formulas for calculating its order are established.

在分配伪格上引入对合反自同构和矩阵M-P逆的概念，得到矩阵M-P逆的若干性质。We introduce the conception of involutorial anti automorphism over distributive pseudolattices, define and get some properties of M-P inverse of matrix.

地图的一个自同构是指基图的一个自同构，且能够扩展成曲面的一个保持定向的自同态。By an automorphism of a map M, we mean an automorphism of underlying graph X which can be extended to an orientation preserving self-homeomorphism of surface.

给出了无限秩仿射李代数的实形和某种类型的紧效实形的定义，并证明了这种紧致实形在自同构下的唯一性。In this paper, we define real form of infinite rank affine Lie Algebra and we also give its some types of compact real form which is proved unique under automorphism.

确定一个群的自同构群和内自同构群的结构往往十分困难，还没有一般性的理论及方法。It is often very difficult to identify the structure of the automorphism group and the inner automorphism group of a group, and there is no general theory and method.

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先讨论一般正交模格簇的次直积的自同构群与自同构群的次直积的关系，再通过自同构映射的性质给出了正交模格MO2的自同构群，利用M。In this paper, the general automorphism groups of products of orthomodular lattices and the products of the automorphism groups of orthomodular lattices MO2 are discussed.

甚至，我们也可以定义一个陪集图是一个图表示，简称GR，即相应的群是否恰等于它的这个陪集图的全自同构群。Further, we can also define if a Coset graph is a graph representation, we note it GR for short, that is, the relevant group is exactly equal to the full automorphism group of the Coset graph.

讨论了齐次循环群的自同态环，进而得到了其自同构群的矩阵描述，最后计算了其自同构群的阶。In this paper, the endomorphism ring of a homocyclic group is studied, and the matrix representation of its automorphism group is given. Finally, the order of its automorphism group is calculated.