自同构

Dade made enormous researches on Coleman automorphism of a finite group and obtained a lot of initial results,especially proved that Coleman outer automorphism group is nilpotent.

E.C.Dade通过对有限群的Coleman自同构的大量研究得到了一系列开创性的结果，最重要的是证明了Coleman外自同构群是幂零群。

On the basis of that, a finite group G satisfying |Aut: Paut|=1, p or pq is successfully classified, where p, q are distinct primes, Aut is the automorphism group of G and Paut is the power automorphism group of G.

然后在此基础上综合运用多方面的知识，进一步给出了满足条件|Aut∶Paut|=1，p或pq的有限群的完全分类，其中Aut是群G的自同构群，Paut是G的幂自同构群，p，q仍是不同的素数。

In the paper,Coleman automorphism is further researched and some properties of Coleman automorphism are obtained.

本文首先对Coleman自同构做了更深入的研究，得到了Coleman自同构的一些性质。

The automorphism groups of the two posets are given and the numbers of orbits of the automorphism groups are counted. At the same time, the number of words in every rank of the posets is obtained.

本章给出了偏序集P和Q的自同构群，计算了在各自的自同构群作用下轨道的个数以及每一轨道中元素的个数，得到了偏序集中每一秩中元素的个数。

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。

All this automorphisms are called standard automorphisms in this paper.

在本文中把这些自同构叫做标准自同构。

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。

In [10] Camina and Siemons classified 2-(υ, 4, 1) designs with a blocktransitive, solvable groups of automorphisms.

对区传递的2-（υ，4，1）设计的分类，Camina和Siemons[10]讨论了自同构群可解的情形，Li[49]讨论了自同构群非可解的情形。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新