两类有限p-群的因子分解数
发布时间：2019-03-25 11:53
【摘要】：在有限群的研究中,利用群的阶数,子群和元素的性质等方面来刻画群的组合问题,一直以来都是研究有限群论的一个重要方向.在关于有限群的组合问题中,研究群的因子分解是一件有趣和有意义的事情,并且该方面的研究与有限群的概率问题有密切地联系.特别地,有限群的子群交换度可以借助于有限群的因子分解数来确定,反之亦然.设G是一个有限群,A和B是G的两个子群,若G=AB,则称G被A和B因子分解.本文主要通过群的阶,元素的阶,莫比乌斯反演公式,Abel p-群的子群数来研究有限p-群的因子分解.本文主要包括三个部分,第一章是介绍有限群的因子分解和有限群子群的交换度的研究背景及意义和一些预备知识.第二章计算一类广义超特殊p-群,即(?),m≥1,的因子分解数.在第三章,计算一类内交换p-群,即(?),n＞m≥1的因子分解数.所用的方法是:先根据子群A,B是否包含导群G'进行分析、计算、讨论,这里分为三种情况,第一种情况,子群A和B都包含导群G';第二种情况,子群A和B都不包含导群G';第三种情况,子群A包含导群G',子群B不包含导群G',反之亦然.然后分别计算出这三种情况中满足条件的G的因子分解数,最后求得G的因子分解数.
[Abstract]:In the study of finite groups, it has always been an important direction to study the combinatorial problem of finite groups by using the order, subgroups and properties of elements to characterize the combinatorial problems of groups. In the combinatorial problem of finite groups, it is interesting and meaningful to study the factorization of groups, and the research in this field is closely related to the probability problem of finite groups. In particular, the degree of subgroup commutation of a finite group can be determined by the factorization number of a finite group, and vice versa. Let G be a finite group and A and B be two subgroups of G. If G is a finite group, then G is decomposed by A and B factors. In this paper, the factorization of finite p-groups is studied by means of the order of groups, the order of elements, the Mobius inversion formula, and the number of subgroups of Abel p-groups. This paper mainly consists of three parts. The first chapter introduces the research background and significance of the factorization of finite groups and the commutation degree of finite group subgroups and some preparatory knowledge. In chapter 2, we calculate the factorization numbers of a class of generalized super-special p-groups, that is, (?), m 鈮，
本文编号：2446948
[Abstract]:In the study of finite groups, it has always been an important direction to study the combinatorial problem of finite groups by using the order, subgroups and properties of elements to characterize the combinatorial problems of groups. In the combinatorial problem of finite groups, it is interesting and meaningful to study the factorization of groups, and the research in this field is closely related to the probability problem of finite groups. In particular, the degree of subgroup commutation of a finite group can be determined by the factorization number of a finite group, and vice versa. Let G be a finite group and A and B be two subgroups of G. If G is a finite group, then G is decomposed by A and B factors. In this paper, the factorization of finite p-groups is studied by means of the order of groups, the order of elements, the Mobius inversion formula, and the number of subgroups of Abel p-groups. This paper mainly consists of three parts. The first chapter introduces the research background and significance of the factorization of finite groups and the commutation degree of finite group subgroups and some preparatory knowledge. In chapter 2, we calculate the factorization numbers of a class of generalized super-special p-groups, that is, (?), m 鈮，
本文编号：2446948
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