幂零群

As is known, groups satisfying central extension conditions are nilpotent.

我们知道满足中心扩张的群是幂零群。

If every minimal p-subgroup of G is containedin Z, every cyclic subgroup of order 4 of G is conditional c-normal in G, then G isp-nilpotent.Theorem 2.3.9 Let p be a fixed prime.

定理2.3.9对某个固定的素数p，设G的每个极小p-子群包含于Z，4阶循环子群在G中条件c-正规，则G是p-幂零的。

At many occasions they arise quite natu-rally.For example,they appear in the Iwasawa decomposition of the isometry group ofa non-compact Riemannian symmetric space.Also,every connected homogeneous Rie-mannian manifold of non-positive sectional curvature can be represented as a connectedsolvable Lie group with a left-invariant Riemannian metric.

它们出现在非紧致黎曼对称空间的等距群的Iwasawa分解中；任一非正截面曲率的连通齐性和黎曼流形可以表为带有左不变黎曼度量的连通可解李群等，带有左不变黎曼度量的幂零及可解李群的微分几何，调和分析和谱几何是重要的研究课题。

Many sufficient and necessary conditions for a finite group to be solvable are given, which generalize some known results.

另一方面，我们研究了Sylow-子群的某些特殊子群的半覆盖远离性对有限群结构的影响，给出了一些有限群为p-幂零和超可解的充分条件。

Many scholars have studied these respects and given many important results, for example, the Hupperts famous theorem, namely, a finite group G is supersolvable if and only if every maximal subgroup of G has prime index; a finite group G is nilpotent if and only if every maximal subgroup of G is normal in G; a finite group G is solvable if and only if every maximal subgroup of G is c-normal in G (See it in [70]); etc.

很多学者都在这些方面进行了研究，得到了很多重要的结果，如：著名的Huppert定理，即有限群为超可解当且仅当它的所有极大子群的指数为素数；有限群为幂零当且仅当每个极大子群都正规；有限群为可解当且仅当它的极大子群均c-正规(见[70])；等等。

We obtain some results on solvability and nilpotency of finite groups by the 9— pairs of 2—maximal subgroups.

利用2-极大子群的θ-子群偶得到了一系列有限群可解，幂零的结果。

One of the cases was showed in theorem 4.18: finite group G is solvable if and only if Sec is nilpotent for every maximal subgroup At without prime index in G.

在本文中作者将要证明：G可解当且仅当对G中的任意极大子群M，或者I中存在极大元C使C/K幂零并且其Sylow2-子群的幂零类≤2，或者Sec为2-闭。

In particular, Bryce, Fedri, Serens and Guo( [2]and[8]) have studied thenilpotent length of the groups in NF \ φ, where φ is the class Y of allsupersoluble groups or the class Nr of groups with nilpotent length ≤r.

特别是，Bryce，Fedri和Serens以及郭([2]和[8])对N~FΦ中的群的幂零长度作出了研究，其中Φ是所有超可解群类Y，或者是幂零长度≤r的群类。

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。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。