In section 4,we research the solvable groups of finite rank,and provethat the union set of all quasi-cyclic subgroups of G is a characteristic subgroup andthe Hirsch number hdoes not exceed n if G is a solvable group of rank n.Inparticular,for an arbitrary solvable torsion-free group G of rank n,we give theupper bound fof the derived length of G.

在第4節(jié)里，我們研究了有限秩的可解群自拍偷拍亚洲专区图片，證明了這類群的所有擬循環(huán)子群構(gòu)成它的一個(gè)特征子群黄情纯女人网站，且對(duì)秩n的可解群G來(lái)說(shuō)，其Hirsch數(shù)h≤n，另外清风阁免费视频A片，我們給出了秩n的無(wú)撓可解群的導(dǎo)出長(zhǎng)度的一個(gè)上界午夜国产黄片免费。

In chapter 1 ,on one hand ,we give some sufficient conditions for a finite group to be supersolvable and nilipotent by using the properties of π-supplemented subgroups;For example: Theorem 3 Let G be a group, 2 ∈π, if every subgroup of G of prime order is contained in SE, every cyclic subgroup of G of order 4 is π-supplemented in G, then G will be supersolvable.

在第一章中，一方面我們利用π-可補(bǔ)子群的性質(zhì)給出了有限群為超可解群及冪零群的若干充分條件自拍四页日韩欧美在线观看；例如：定理3設(shè)G是群国产玩弄老太婆，2∈π，如果G的每個(gè)素?cái)?shù)階子群包含在SE中呻吟av影院，G的每個(gè)4階循環(huán)子群在G中π-可補(bǔ)操操操b，則G為超可解群。

Let F=LF be a s-closed local formation such that every minimal non-F-groups is solvable. It is proved that 1 If every cyclic subgroup of of order 4 and every minimal subgroup of G are contained in, then G is a F-group. 2 If there exists a normal subgroup N of G such that G/N∈F and every cyclic subgroup of N of order 4 is weakly c-normal in G and every element of N of prime order is contained in Z(superscript f subscript ∞), then G is a F-group.

設(shè)F=LF是一個(gè)子群閉的局部群系男女无遮挡毛片视频免费，滿足每個(gè)極小非F-群是可解群免费看一级A片在线看手机，證明了：1如果G的任意極小子群和任意4階循環(huán)子群都含于Z中，那么G是F-群亚洲精品性爱视频；2如果存在G的正規(guī)子群国内自拍和偷拍，使得G/N∈F，且N的任一4階循環(huán)子群在G中弱c-正規(guī)又污又色又吃胸的视频，N的任一素?cái)?shù)階元含于Z中91.com麻豆，那么G是F-群。

We showed that if G is a non-perfect 11-decomposable finite group, then G is isomorphic to an Abel group of order 121, or a non-Abel group of order pq, here p, q are primes which satisfy p-1-=10q or p=11, q=,r is a prime, too.

在本章中主要證明了日本黄色网站一级片，11-可分解的有限可解群国产女同精品一区二区三区，必同構(gòu)于121階Abel群：或同構(gòu)于pq階非Abel群，其中p外国黄色视频九九，q均為素?cái)?shù)182黄色网站入口，且滿足p-1=10q或p=11，q=91精品一区在线观看？

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.

讀這本書之前亚洲综合伊人精品推荐，讀者需要一些有限群論的基本知識(shí)，如Sylow定理及其應(yīng)用成熟男女性满足视频，置換群www.ggzhyc.com，可解群和冪零群的基本性質(zhì)等等。

Then G∈U.③ If every subgroup of prime order or of order 4 of a group G has a U-s-supplement or be S-quasinormal in G. then G is supersoluble.

若群G的每個(gè)素?cái)?shù)階子群和4階循環(huán)子群在G中或有U-s-補(bǔ)充一级黄片;一被-，或?yàn)镾-擬正規(guī)，則G為超可解群国产精品免费观看91。

In this paper, the author gives sufficient and necessary condition of solvable group using the weak c-normality of maximal and Sylow subgroup and gets some results about supersolvability and p-nilpotentlity of groups

作者研究了弱c-正規(guī)的性質(zhì)并用Sylow子群和極大子群的弱c-正規(guī)性來(lái)確定一些群的結(jié)構(gòu)女人自慰喷水的网站，給出了一個(gè)群為可解群的充分必要條件，同時(shí)由極大子群乱伦视频APP、Sylow子群的弱c-正規(guī)性得到群G p-冪零国产性行为视频、超可解的有關(guān)定理。

We first characterize the groups in which all m∈cdq〓 contain at most 4 prime divisors; and then show the following: if any m∈cdq〓 is nth-power-free then the derived length of solvable group G is bounded by a function f depended only on n; also if cdq〓 has k different p-parts then the p-length of solvable group G is bounded by a function g depended only on k.

首先研究了非線性不可約特征標(biāo)對(duì)應(yīng)的特征標(biāo)次數(shù)的商至多含有4個(gè)素因子的有限群結(jié)構(gòu)久久AV先锋影音资源网站。其次久久这里精品12，我們證明：若每m∈cdq〓是n次方自由的国产手机小视频看片，則有限可解群G的的導(dǎo)長(zhǎng)及p-長(zhǎng)都被僅依賴于n的函數(shù)所界定；若cdq〓中共有k個(gè)兩兩不同的p-部分国产专区网站，則有限可解群G的p-長(zhǎng)能被僅依賴于k的函數(shù)所界定欧美一级情欲视频。

Finite group; conditional c-normal; solvable group; p-supersolvable group; p-nilpotent group

基礎(chǔ)科學(xué)，數(shù)學(xué)美女黄色福利视频，代數(shù)女同一区二区三区、數(shù)論、組合理論有限群欧美日韩国产中文在线专区视频；條件c-正規(guī)子群免费性爱a片在线；可解群； p-超可解群精品拍拍； P-冪零群

A sufficient condition for supersolvable group depending on theproperty π-quasinormal of its Fitting subgroup is given.

聶林通過(guò)討論有限群的Fitting子群的極小子群的π-擬正規(guī)性AV网站大全免费，利用有限群的正規(guī)群列及多種有限群論的方法和技巧，得到了一個(gè)有限的可解群成為超可解的充分條件欧美视频在线观看图片小说。

connected solvable group：連通可解群

連通集|connected set | 連通可解群|connected solvable group | 連通空間|connected space

locally soluble group：局部可解群

locally separable space 局部可分空間 | locally soluble group 局部可解群 | locally trivial embedding 局部平凡嵌入

solvable group：可解群

solvable equation 可解方程 | solvable group 可解群 | solvable ideal 可解理想

topologically solvable group：拓?fù)淇山馊?/p>

topologically ringed space 拓?fù)洵h(huán)式空間 | topologically solvable group 拓?fù)?strong>可解群 | topologico differential invariant 拓?fù)湮⒎植蛔兪?/p>

topologically solvable group：拓?fù)淇山馊簾o(wú)憂雅思網(wǎng)

topologically solvable group 拓?fù)?strong>可解群無(wú)憂雅思網(wǎng)tww2a+B | topologico differential invariant 拓?fù)湮⒎植蛔兪綗o(wú)憂雅思網(wǎng)_L+gT4f | topologize 拓?fù)浠療o(wú)憂雅思網(wǎng)*BS'\\leoI9T

locally solvable group：局部可解群

局部單連通的 locally simply connected | 局部可解群 locally solvable group | 局部全有界群 locally totally bounded group

finite solvable group：有限可解群

finite solution 有限解 | finite solvable group 有限可解群 | finite space 有限空間

solvable groups：可解群

冪零群:Nilpotent groups | 可解群:Solvable groups | 超可解:supersolvable groups

soluble subgroups：可解群

水溶性:Water-soluble | 可解群:soluble subgroups | 心房顫動(dòng):soluble

supersolvable group：超可解群

superset 超集 | supersolvable group 超可解群 | supervisor 管理程序