正规子群

Li and one of his lemmas toabbreviate the nonnormal Cayley digraph 〓 into the case when 〓 is a dicycle.When 〓 is a dicycle,we give the sufficient and necessary conditions for 〓 to benonnormal and the structure of the corresponding automorphism group Aut.

Li定义的一个图〓，其中N是Aut的一个非平凡极小正规子群，和他的一个引理，把对非正规Cayley有向图Γ的讨论简化到〓是一个有向圈的情况，进而决定了当〓为有向圈时，Γ非正规的充要条件和Aut的结构。

When form ring satisfies certain Λ-stable range condition, we use the results in [2]to prove the normality of a unitary congruence subgroup EU andan important commutator equation of unitary congruence subgroups.

在型环满足适当的Λ-稳定秩条件时，利用[2]中的结果证明了酉群的同余子群EU的正规性，建立了酉群的同余子群之间的一个换位子公式。

In § 1, we give main definitions and basic results that are needed in the paper. In § 2, we determine the structures of somegroups by using s-normality of Sylow subgroups and the maximal subgroups of Sylow subgroups. There are the main theorems that 1 Let G be a finite group and P be a Sylow p-subgroup of G where p is a prime divisor of |G|.

我们在§1中将给出本文所需的主要概念和基本结果，在§2中讨论Sylow子群、Sylow子群的极大子群的s-正规性对群的结构的影响，主要结果是1设G为有限群，p为|G|的素因子，P为G的Sylow p-子群。

The semigroup algebra theory,which has a huge development under interior and exterior double Mathematical conditions form 1950"s to 1960"s,is a new branch of algebra theory.In 1990,R.Biswas gave definition of anti-fuzzy subgroup.In 1995,Shen gave definitions of anti-fuzzy subgroup and normal anti-fiizzy subgroup of group.

半群的代数理论是在数学内部和外部双重条件下，从20世纪50年代到60年代发展起来的一个崭新的代数分支。1990年，Biswas R提出了反Fuzzy子群的定义；1995年沈正维提出了一个群的反Fuzzy子群和正规反Fuzzy子群的定义。

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-正规的性质并用Sylow子群和极大子群的弱c-正规性来确定一些群的结构，给出了一个群为可解群的充分必要条件，同时由极大子群、Sylow子群的弱c-正规性得到群G p-幂零、超可解的有关定理。

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.

本文结合有限群的某些特殊子群(如，极小子群，极大子群，Sylow子群，Sylow子群的极大子群)的条件c-正规性来研究有限群的可解性，超可解性，幂零性，得到了有限群可解，超可解，幂零的若干充分和充要条件，推广了有限群的一些结果。

Where HSG is the maximal subnormal subgroup of G which is contained in H.

其中HSG表示G包含在H中的最大的次正规子群。

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

聂林通过讨论有限群的Fitting子群的极小子群的π-拟正规性，利用有限群的正规群列及多种有限群论的方法和技巧，得到了一个有限的可解群成为超可解的充分条件。

A subgroup of a finite group G is called π-quasinormal in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be c-supplemented in G if there exists a subgroup N of G such that G=HN and H∩N≤H=Core.

有限群G的一个子群称为在G中是π-拟正规的若它与G的每一个Sylow-子群是交换的。G的一个子群H称为在G中是c-可补的若存在G的子群N使得G=HN且H∩N≤H＝Core。

To ensure the normal handling of religious affairs by religious personages, the government grants stipends to those who are in financial difficulties

为保证宗教人士正常地履行教务，政府对一些生活困难的宗教人士，发放一定的生活补助费。正规子群，不变子群

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐