共轭置换与有限群结构
发布时间：2019-07-01 15:01
【摘要】：本文结合有限群G的某些特殊子群(如Sylow子群,极大子群以及Sylow子群的极大子群)的共轭置换性,半正规性及C-正规性来讨论有限群的结构.我们共讨论了三类问题,主要内容如下：第一类,讨论了因子群的Sylow子群的R-共轭置换性对有限群结构的影响.即设G为有限群,A,B以及R为G的子群且满足G=AB.根据R-共轭置换子群的概念,我们研究了G的幂零性与A,B的Sylow子群的R-共轭置换性之间的关系.第二类,讨论了极大子群(2-极大子群)共轭置换性、半正规性与有限群结构的关系.即结合共轭置换子群与半正规子群的概念,当群G的极大子群(2-极大子群)或共轭置换或半正规时,本文研究了这一条件与群G的超可解性之间的关系.第三类,综合Sylow子群及极大子群的研究,我们讨论了Sylow子群的极大子群的共轭置换性与有限群结构的关系.即结合共轭置换子群与半正规子群(C-正规子群)的概念,本文研究了群G的Sylow子群的极大子群或共轭置换或半正规(C-正规)这一条件与群G的超可解性之间的关系.
[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，
本文编号：2508580
[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，
本文编号：2508580
本文链接：https://www.wllwen.com/kejilunwen/yysx/2508580.html
