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.

在第一章中免费欧美一级A片，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；例如：定理3設(shè)G是群天天爽天天插夜夜摸日日干，2∈π亚洲色图国产，如果G的每個(gè)素?cái)?shù)階子群包含在SE中，G的每個(gè)4階循環(huán)子群在G中π-可補(bǔ)日本免费一级高清婬日本片欧美，則G為超可解群CaoPoron草棚在线视频。

Many sufficient and necessary conditions for a finite group to be solvable are given, which generalize some known results.

另一方面，我們研究了Sylow-子群的某些特殊子群的半覆蓋遠(yuǎn)離性對(duì)有限群結(jié)構(gòu)的影響丰满又黄又爽少妇毛片，給出了一些有限群為p-冪零和超可解的充分條件免费进入黄色网站。

Many scholars have studied these respects and given many important results, for example, the Hupperts famous theorem, namely, a finite group G is supersolvable if and only if every maximal subgroup of G has prime index; a finite group G is nilpotent if and only if every maximal subgroup of G is normal in G; a finite group G is solvable if and only if every maximal subgroup of G is c-normal in G (See it in [70]); etc.

很多學(xué)者都在這些方面進(jìn)行了研究，得到了很多重要的結(jié)果色色婷婷色婷色色，如：著名的Huppert定理日韩一区二区在线视频观看，即有限群為超可解當(dāng)且僅當(dāng)它的所有極大子群的指數(shù)為素?cái)?shù)；有限群為冪零當(dāng)且僅當(dāng)每個(gè)極大子群都正規(guī)www.99riav.com；有限群為可解當(dāng)且僅當(dāng)它的極大子群均c-正規(guī)(見(jiàn)[70])国产精品视频一区二区三区无码乱伦；等等。

In particular, Bryce, Fedri, Serens and Guo( [2]and[8]) have studied thenilpotent length of the groups in NF \ φ, where φ is the class Y of allsupersoluble groups or the class Nr of groups with nilpotent length ≤r.

特別是尤物在线无码视频观看网址，Bryce女优网址，F(xiàn)edri和Serens以及郭([2]和[8])對(duì)N~FΦ中的群的冪零長(zhǎng)度作出了研究，其中Φ是所有超可解群類Y欧美日韩国内，或者是冪零長(zhǎng)度≤r的群類青草视频免费。

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，或?yàn)镾-擬正規(guī)国产亚洲精品ⅴa在线观看，則G為超可解群国产色清。

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)，給出了一個(gè)群為可解群的充分必要條件亚洲一区免费视频，同時(shí)由極大子群作爱超A级黄色视频、Sylow子群的弱c-正規(guī)性得到群G p-冪零、超可解的有關(guān)定理亚洲国产一区二区三区。

In this paper, by using conditional cnormalityof some special subgroups(such as minimal subgroups, maximal subgroups, Sylowsubgroups, maximal subgroups of Sylow subgroups)of G, we obtain some sufficient or necessaryconditions for a finite group to be solvable, supersolvable, nilpotent. Some previouslyknown results are generalized.

本文結(jié)合有限群的某些特殊子群(如欧美日韩在线观看二区视频，極小子群，極大子群亚洲中文九九九，Sylow子群自拍视频偷拍天堂，Sylow子群的極大子群)的條件c-正規(guī)性來(lái)研究有限群的可解性国产三级精品三级，超可解性，冪零性五月综合色色，得到了有限群可解思思99re6精品视频免费观看，超可解，冪零的若干充分和充要條件国模AⅤ私拍一区二区，推廣了有限群的一些結(jié)果最新在线国产。

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

基礎(chǔ)科學(xué)，數(shù)學(xué)欧美一级特黄大片在线播放一，代數(shù)一级特黄AAA片免费女、數(shù)論、組合理論有限群久草性爱中文黄片免播；條件c-正規(guī)子群欧洲黑人黄片；可解群； p-超可解群色久悠悠中文字幕； 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，利用有限群的正規(guī)群列及多種有限群論的方法和技巧无码精品日韩网站视频，得到了一個(gè)有限的可解群成為超可解的充分條件精品自拍第2页在线。

The authors use the condition that some subgroups of a finite group G has a U-s-supplement or be S-quasinormal in G, to give some conditions under which the group G is supersolvable and generalize some of these results into formations.

利用群G的某些子群在G中或有F-s-補(bǔ)充，或?yàn)镾-擬正規(guī)视频一区视频在线，給出有限群為超可解的若干充分條件私人福利影院，并將其中的一部分結(jié)果推廣到群系中。

solvable groups：可解群

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

supersolvable group：超可解群

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