【摘要】：本文結(jié)合有限群G的某些特殊子群(如Sylow子群,極大子群以及Sylow子群的極大子群)的共軛置換性,半正規(guī)性及C-正規(guī)性來(lái)討論有限群的結(jié)構(gòu).我們共討論了三類(lèi)問(wèn)題,主要內(nèi)容如下：第一類(lèi),討論了因子群的Sylow子群的R-共軛置換性對(duì)有限群結(jié)構(gòu)的影響.即設(shè)G為有限群,A,B以及R為G的子群且滿(mǎn)足G=AB.根據(jù)R-共軛置換子群的概念,我們研究了G的冪零性與A,B的Sylow子群的R-共軛置換性之間的關(guān)系.第二類(lèi),討論了極大子群(2-極大子群)共軛置換性、半正規(guī)性與有限群結(jié)構(gòu)的關(guān)系.即結(jié)合共軛置換子群與半正規(guī)子群的概念,當(dāng)群G的極大子群(2-極大子群)或共軛置換或半正規(guī)時(shí),本文研究了這一條件與群G的超可解性之間的關(guān)系.第三類(lèi),綜合Sylow子群及極大子群的研究,我們討論了Sylow子群的極大子群的共軛置換性與有限群結(jié)構(gòu)的關(guān)系.即結(jié)合共軛置換子群與半正規(guī)子群(C-正規(guī)子群)的概念,本文研究了群G的Sylow子群的極大子群或共軛置換或半正規(guī)(C-正規(guī))這一條件與群G的超可解性之間的關(guān)系.
[Abstract]:In this paper, we discuss the structure of finite groups by combining the conjugated permutation, seminormality and C-normality of some special subgroup of finite group G (such as Sylow subgroup, maximum subgroup and maximum subgroup of Sylow subgroup). In this paper, we discuss three kinds of problems, the main contents are as follows: first, we discuss the influence of R-Conjugate substitution of Sylow subgroup of factor group on the structure of finite group. Suppose G is a finite group, A, B and R are subgroup of G and satisfy G 鈮，

本文編號(hào)：2508580