正规子群

Group, Subgoup, Permutation Group, Cyclic Group, Commutative Group, Normal Subgroup, Factor Group, Isomorphism, Ring, Ideal, Field, Polynomial Ring, Factor Ring.

课程内容：群，子群，置换群，循环群，交换群，正规子群，商群，群之同构，环，理想，体，多项式环，商环等。

Let F=LF be a s-closed local formation such that every minimal non-F-groups is solvable. It is proved that 1 If every cyclic subgroup of of order 4 and every minimal subgroup of G are contained in, then G is a F-group. 2 If there exists a normal subgroup N of G such that G/N∈F and every cyclic subgroup of N of order 4 is weakly c-normal in G and every element of N of prime order is contained in Z(superscript f subscript ∞), then G is a F-group.

设F=LF是一个子群闭的局部群系，满足每个极小非F-群是可解群，证明了：1如果G的任意极小子群和任意4阶循环子群都含于Z中，那么G是F-群；2如果存在G的正规子群，使得G/N∈F，且N的任一4阶循环子群在G中弱c-正规，N的任一素数阶元含于Z中，那么G是F-群。

Subgroup, Factor Group, Isomorphism, Ring, Ideal, Field, Polynomial Ring, Factor

课程内容：群，子群，置换群，循环群，交换群，正规子群，商群，群之同构，环，理想，体，多项式环，商环等。

In this paper, some more properties of the existence and conjugacy of complements of a normal subgroup K of a finite group G are studied.

研讨了关于有限群G的一个正规子群K的补子群之存在性与共轭性的更多一些的结果。

This article proves that in the homomorphism of G onto ■,the inverse image of a maximal normal subgroup in ■ is also a maximal normal subgroup in G.

本文得到了在同态满射下，极大正规子群的逆象也是极大正规子群，并给出了极大正规子群的象也是极大正规子群的一些等价条件。

For a Hall π-subgroup in π-separable group and a given π-Fong character, we show that there always exists a normal subgroup, such that some irreducible constituent of this π-Fong character which restricts on the join of these two subgroups is a π-Fong character associated to this normal subgroup.

对于π-可分群的一个Hall π-子群和一个给定的π-Fong特征标，我们证明了总存在一个正规子群使得这个π-Fong特征标在这两个子群的交上的限制的某个不可约成分是联系这个正规子群的一个π-Fong特征标。

Subgroup H of G is said to be π-quasinormally embedded in G, if for each prime divisor p of the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some π-quasinormal subgroup of G.

bstract 设G是有限群，称G的子群H在G中π-拟正规嵌入，如果对于{H}的每个素因子p， H的Sylow p-子群也是G的某个π-拟正规子群的Sylow p-子群。

A subgroup H of G is said to be π-quasinormally embedded in G, if for each prime divisor p of the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some π-quasinormal subgroup of G.

设G是有限群，称G的子群H在G中π-拟正规嵌入，如果对于{H}的每个素因子p， H的Sylow p-子群也是G的某个π-拟正规子群的Sylow p-子群。

Starting from the definition of almost normal subgroup , the author gives some interesting results about almost normal subgroups and the sufficient conditions for a finite group to be solvable.

利用几乎正规的定义对有限群G作了一些研究，得到了几乎正规子群的一些性质，并给出了有限群为可解群的几个充分条件。

We know that the concept of c-normal subgroup is related to the concept of normal subgroup.

我们知道c-正规子群的概念是与子群的正规性有关的。

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