查询词典 automorphism group

Kimmerle proved that Coleman outer automorphism group is abelian and gave some sufficient conditions on the group being a p — group and trivial group.

Kimmerle又证明了该群还是交换群，而且他们给出了Coleman外自同构群是p'-群的一些充分条件和该群为平凡群的情况。

A finite p-group G is called LA-group, if the order of G divides the order of the automorphism group of G.

称有限p-群G是LA-群，如果群G的阶能整除群G的自同构群的阶。

Automorphism group of a linear code is obtained with the help of the general linear group constructed by all invertible matrices, and it is illustrated by matrices generalized inverses.

给出了通过求解可逆矩阵构成的一般线性群，获得线性码的自同构群的方法，并利用矩阵广义逆理论，对线性码的自同构群进行进一步刻划。

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.

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。

Automorphism group of a linear code is obtained with the help of the general linear group constructed by all invertible matrices,and it is illustrated by matrices generalized inverses.

文 [1 ]给出了判断一个置换矩阵是否属于自同构群的充分必要条件，文 [4]在此基础上利用矩阵广义逆理论对自同构群进行研究得出了一些有用的结论。

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。

linear code ; permutation group ; automorphism group ; generalized inverse

根据线性码生成矩阵的性质，可以简化自同构群的计算；b 。

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。

Let G be a finite group, and S a subset of G not containing theidentity element 1. The Cayley digraph Cay on G with respect to S is definedas a directed graph with vertex set G and edge set {|g∈G, s∈S}. IfS~(-1)=S, then Cay is undirected and in this case, we view two directededges and as an undirected edge {u, v}. Obviously, the right regularrepresentation R of G, the acting group of G by right multiplication, is asubgroup of the full automorphism group AutCay(G, S of Cay.

给定有限群G，设S是G的不含单位元1的子集，群G关于子集S的Cayley有向图Cay是一个以G顶点集合，而以｛|g∈G，s∈S｝为边集合的有向图，特别地，若S~(-1)=S，则X=Cay是无向的，此时我们把一条无向边｛u，v｝等同于两条有向边和，易见，群G的右正则表示R，即G在G上的右乘作用，为图Cay的全自同构群AutCay

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)。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。