内自同构

Lubotski [3] and Lue [2] showed that every normal automorphism of a non-cyclic free group is inner.

Lubotski[3]和Lue[2]证明了秩不小于2的自由群的每个正规自同构都是内自同构。

The new method has two key steps: one is to get the automorphism group of HEm, and the another one is to introduce the concept of semi-Reinhardt domain and get its complete orthonornal system.

关键之处有两点：一是给出第三类华罗庚域的全纯自同构群，群中每一元素将形为(W，Z0)的内点映为点(W*，0)；二是引进了semi—Reinhardt的概念并求出了其完备标准正交函数系。

Moreover, some subgroups of Aut are obtained, such asthe inner automorphism group, the central automorphism group, the involutional automorphism group, the first and the second extremal automorphism group.

证明了：当n=0时，Aut中每个元素都是内自同构，且Aut≌C(定理1.12)。n=1时，Aut中每个元素都是有限个内自同构，中心自同构，对合自同构和第一类外自同构的乘积(定理1.13)。

Holomorphic vectors and holomorphic automorphism groups of a sort of three-dimensional Hopf manifold

本文确定了亚循环的内交换p-群(p≠2)的自同构群的阶，并给出了其自同构群的结构。

The major technique to get the information of structure of those free groups is to sudy the action of automorphisms on them. In this paper we show that every normal automorphism of a nontrivial free product of groups is inner as well. Traub[16] made a purely algebraic conjecture and showed that it implied Poincare"s Conjecture. He also showed that Poincare"s Conjecture implied this algebraic conjecture modulo another topological hypothesis.

在本文中我们给出任意两个非平凡群的自由积的每个正规自同构也是内自同构的；在文献[16]中，Traub给出了一个纯代数的猜想并证明了这个猜想蕴含着着庞加莱猜想的成立，并且作者也证明了在一个拓扑假设的前提下庞加莱猜想也同时蕴涵着猜想1是成立的，后来这个拓扑假设被Waldhausen([7])证明是成立的。

In chapter 3,we will consider the automorphisms of triangular matrix algebras over commutative semirings.

利用矩阵的一些性质，克服了环上可逆矩阵在半环中未必可逆的难点，证明交换半环R上的n阶三角矩阵代数Tn的自同构都是内自同构。

In 1927,Skolem obtained the famous Skolem-Noether theory:the automorphisms of the n × n matrix algebra over a field are inner.

早在1927年，Skolem就获得了著名的Skolem-Noether定理：域上的矩阵代数的自同构皆为内自同构。

By using properties of scalar matrices over semirings,we generalize algebraic properties for the automorphisms of matrix algebras over commutative rings and obtain some algebraic properties for the automorphisms of matrix algebras over commutative semirings.

在这一章中，我们首先利用半环上常量矩阵的性质把环上矩阵代数的性质拓广到半环上，获得了交换半环上矩阵代数自同构的一些代数性质，接下来采用积和式的方法证明任意非负交换半环上n阶矩阵代数Tn的自同构的n次幂必为内自同构。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失