查询词典 solvable group

We know that the solutions of quadratic, cubic and quartic can be expressed by radicals. As to the solution of the quintic which has became an issue for past two or three hundred years, it was not solved until 1832 a great young Mathematician of French named Galois who recommended group theory that proved a polynomial of degree 5 and over 5 can't be solvable by radicals.

中文摘要我们知道二次、三次及四次的方程式都可以用根式表示，至於五次方程式的解迟迟无法解决，这个问题持续了两三百年，直到1832年，一位法国青年Galois在其决斗前夕，在他的遗书中，这位伟大的青年数学家引进了群的理论，证明了：五次及五次以上的方程式，不可能有公式解。

The reader will need to know some basic finite group theory: the Sylow theorems and how to use them and some elementary properties of permutation groups and solvable and nilpotent groups.

读这本书之前，读者需要一些有限群论的基本知识，如Sylow定理及其应用，置换群，可解群和幂零群的基本性质等等。

One of the cases was showed in theorem 4.18: finite group G is solvable if and only if Sec is nilpotent for every maximal subgroup At without prime index in G.

在本文中作者将要证明：G可解当且仅当对G中的任意极大子群M，或者I中存在极大元C使C/K幂零并且其Sylow2-子群的幂零类≤2，或者Sec为2-闭。

Theorem3 G is a formal set p~n q of p -order subgroup of solvable simple group meeting, P is Sylowp -subgroup of G .

定理3设G是有正规p -子群的p~n q阶可解次单群， P是G的Sylowp -子群。

And then with the help of the IP -groups' constructions, studies will be centered on its nature, and its relations with the finite solvable subsimple group and the finite groups in which every element has prime order and applying the two principles on IP -groups.

随后利用IP -群的结构，重点来研究其性质，指出它与可解有限次单群、质元群之间的包含关系，并且将质元群中的两个重要性质推广到IP -群中。

Linear equations the main issues discussed are:① When a group of equations solvable.

线性方程组主要讨论的问题是：①一个方程组何时有解。

Theorem 3.2 Let G be a solvable finite group.

定理3.2 设G为有限可解群。

Starting from the definition of almost normal subgroup , the author gives some interesting results about almost normal subgroups and the sufficient conditions for a finite group to be solvable.

利用几乎正规的定义对有限群G作了一些研究，得到了几乎正规子群的一些性质，并给出了有限群为可解群的几个充分条件。

By using the c-supplementation of Sylow 2-subgroup and Sylow 3-subgroup, we obtain two sufficient and necessary conditions for a finite group to be solvable.

利用Sylow 2-子群和Sylow 3-子群的c-可补性得到有限群成为可解的两个充要条件，推广了几个已知的定理。

Thus we extend the works by Fan and Humphreys independently on polycyclicgroups.In section 3,we prove that 〓 if G is a solvable non-torsion group ofrank 3.This extends a result of McCutcheon who proved it only for polycyclicgroups.

在第3节里，我们讨论了秩3的可解群，证明了当这类群含有无限阶元时，其导出长度至多为6，但在挠群的场合，其导出长度是不能界定的，这推广了McCutcheon的一个结果。

Since historical times,England ,where the early inhabitants were Celts, has been conquered three times .

从有历史以来，英国，在此地早期居住的是凯尔特人，已经被征服了三次。

Bluetooth OBEX File Transfer Enables the sending and receiving of files on your phone via Bluetooth.

蓝牙OBEX文件移动允许经过蓝牙传送和接受文件。。。。