本文選題：弱M-可補(bǔ)性 + S-半置換性��； 參考：《上海大學(xué)》2017年博士論文

【摘要】：在有限群論中,應(yīng)用子群在有限群中的嵌入性質(zhì)來(lái)研究有限群的結(jié)構(gòu)是人們非常感興趣的課題.由于子群的正規(guī)性與可補(bǔ)性是有限群論中最基本的性質(zhì),于是由此引出許多與它們相關(guān)的嵌入性質(zhì),并且人們已經(jīng)獲得大量的研究成果.本文將繼續(xù)這一領(lǐng)域的研究,重點(diǎn)研究素?cái)?shù)冪階子群在有限群中的嵌入性質(zhì),獲得了一些有價(jià)值的成果.在第三章,我們主要利用素?cái)?shù)冪階子群的弱M-可補(bǔ)性,獲得了有限群G的某個(gè)正規(guī)子群包含在G的F-超中心ZF(G)中的一些充分條件,其中F是一個(gè)包含超可解群類(lèi)u的可解飽和群系.在第四章,我們通過(guò)研究Op(G)的d階非循環(huán)子群的S-半置換性,獲得了包含在有限群G的某個(gè)正規(guī)P-子群中的C-主因子都循環(huán)的充分條件及G的結(jié)構(gòu)的相關(guān)信息,其中d為素?cái)?shù)P的某個(gè)方冪.在第五章,我們首先引入子群的一個(gè)新的嵌入性質(zhì),即:Π*-性質(zhì),然后從素?cái)?shù)冪階子群的Π*-性質(zhì)出發(fā),獲得了有限群G的某個(gè)正規(guī)子群E在G中p-超循環(huán)嵌入的充要條件,其中P ∈ π(E).作為上述研究的繼續(xù),我們考察了有限群G的Ap-1-剩余GAp-1,其中Ap-1是冪指數(shù)整除P- 1的交換群類(lèi).我們不僅給出了GAp- 的基本性質(zhì),而且通過(guò)研究Op(GAp-1)的給定階特殊子群在G中的嵌入性質(zhì),獲得了有限群G為P-超可解群等若干結(jié)果.
[Abstract]:In finite group theory, it is of great interest to study the structure of finite groups by applying the embedding property of subgroups in finite groups. Since the normality and complementarity of subgroups are the most basic properties in finite group theory, many embedded properties related to them are derived, and a lot of research results have been obtained. In this paper, we will continue to study the embedding properties of prime power order subgroups in finite groups, and obtain some valuable results. In chapter 3, we obtain some sufficient conditions for a normal subgroup of a finite group G to be contained in the F-supercenter of G by using the weak M-complement of a prime power subgroup. Where F is a solvable saturated formation containing the class u of a supersolvable group. In chapter 4, by studying the S- semipermutation of non-cyclic subgroups of order d of Opg, we obtain the sufficient conditions of C- principal factor cycles in a normal P- subgroup of a finite group G and the relevant information about the structure of G. Where d is a power of the prime number P. In chapter 5, we first introduce a new embedding property of a subgroup, that is, a 蟺 -property. Then we obtain a sufficient and necessary condition for a normal subgroup E of a finite group G to be phypercyclic embedded in G. Where P 鈭，

本文編號(hào)：1938244