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.

在第一章中欧美淫欲视频，一方面我們利用π-可補子群的性質(zhì)給出了有限群為超可解群及冪零群的若干充分條件婷婷丁香五月一区二区三区；例如：定理3設(shè)G是群，2∈π午夜免费A级毛片试看，如果G的每個素數(shù)階子群包含在SE中看毛片视频，G的每個4階循環(huán)子群在G中π-可補，則G為超可解群99久久久免费毛片。

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

另一方面v视界影院，我們研究了Sylow-子群的某些特殊子群的半覆蓋遠離性對有限群結(jié)構(gòu)的影響，給出了一些有限群為p-冪零和超可解的充分條件欧美cao。

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)者都在這些方面進行了研究三级国产网站，得到了很多重要的結(jié)果欧美专区福利，如：著名的Huppert定理，即有限群為超可解當且僅當它的所有極大子群的指數(shù)為素數(shù)亚洲曰本无码av中文字幕；有限群為冪零當且僅當每個極大子群都正規(guī)日本乱人伦视频一区二区三区；有限群為可解當且僅當它的極大子群均c-正規(guī)(見[70])；等等欧美老妇操逼大片。

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.

特別是精品免费观看69影院，Bryce，F(xiàn)edri和Serens以及郭([2]和[8])對N~FΦ中的群的冪零長度作出了研究免费播看30分钟大片，其中Φ是所有超可解群類Y国产视频色色色，或者是冪零長度≤r的群類。

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的每個素數(shù)階子群和4階循環(huán)子群在G中或有U-s-補充男女黄色网站视频，或為S-擬正規(guī)色色色综合五月天，則G為超可解群。

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)性來確定一些群的結(jié)構(gòu)99尤物无码国产福利在线观看，給出了一個群為可解群的充分必要條件干逼视频，同時由極大子群、Sylow子群的弱c-正規(guī)性得到群G p-冪零殴美aaaav、超可解的有關(guān)定理99久久国产亚洲精品观看。

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，極小子群114毛片，極大子群91三级片在线，Sylow子群，Sylow子群的極大子群)的條件c-正規(guī)性來研究有限群的可解性欧美视频大全，超可解性自拍偷拍25页，冪零性，得到了有限群可解国产三级网片，超可解密黄片啪啪啪，冪零的若干充分和充要條件，推廣了有限群的一些結(jié)果午夜福利在线视频观看在线。

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

基礎(chǔ)科學(xué)日韩资源在线观看快射视频免费，數(shù)學(xué)，代數(shù)真人黄色网站入口免费、數(shù)論91精品熟女另类、組合理論有限群；條件c-正規(guī)子群偷拍播放；可解群欧美黄色网站视频免费1000； p-超可解群； P-冪零群

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

聶林通過討論有限群的Fitting子群的極小子群的π-擬正規(guī)性4444www免费看，利用有限群的正規(guī)群列及多種有限群論的方法和技巧亚洲视频热热，得到了一個有限的可解群成為超可解的充分條件五月天色色香蕉。

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-補充，或為S-擬正規(guī)久久黄色视频看一下，給出有限群為超可解的若干充分條件欧美久久久久，并將其中的一部分結(jié)果推廣到群系中。