1) Minimal-non M-groups
极小非超可解群
2) π _solvable minimal not Γ k-π n group
π-可解极小非Γ_k-πn群
3) supersolvable group
超可解群
1.
Sufficient and necessary conditions for supersolvable group;
超可解群的若干充要条件
2.
Using the weakly c-normality of minimal subgroup of to characterize the structure of a finite group,some sufficient conditions of finite supersolvable group are obtained.
利用极小子群的弱c-正规性刻画了有限群的结构,得到了有限超可解群的若干充分条件;从群系理论出发,得到了包含超可解群类的饱和群系的充分条件,并推广了一些已知结果。
3.
In this paper we prove:Let F be a saturated formation containing U,the class of all supersolvable groups and suppose that G is a group with a normal subgroup H such that G/H∈F.
本文证明了:设F是一个包含超可解群系U的饱和群系,G有一个正规子群H使得G/H∈F。
4) supersoluble group
超可解群
1.
The completely conditional permutability of minimal subgroups is used in this paper to obtain the sufficient condition for supersoluble groups: let G be a finite group, if every minimal subgroup and every cyclic subgroup of order 4 of G is completely c-permutable in G, G is supersoluble.
利用极小子群的完全条件置换性给出了超可解群的一个充分条件 :设 G是一个群 ,如果 G的每个极小子群和每个 4阶循环子群都是 G的完全条件置换子群 ,则 G是一个超可解
2.
Using the concept,X-permutable subgroup of finite groups,two sufficient conditions of supersoluble groups are obtained:(1) G is a soluble group,let X be a subgroup of G such that X contains every maximal subgroup and every minimal subgroup of G.
如果G的每个极大子群和G的sylow子群的每个极大子群在G中X-可换,那么G是超可解群;(2)设K■G,X是G的子集且包含G的p-子群。
3.
In this paper,by using the concept of permutable subgroups,a new criterion of supersolubility of the product G=AB of finite supersoluble groups A and B is given.
利用子群的可置换性,给出了两个超可解子群A和B的乘积仍为超可解群的一个判别准则。
5) supersolvable groups
超可解群
1.
This paper assumes that every non-cyclic Sylow subgroup P of G has a subgroup D such that 1<|D|<|P| and all subgroups H of P with order |H|=|D| and with 2|D|(if P is a non-abelian 2-group and |P:D|>2) are normally embedded in G,and some sufficient conditions are obtained on G to be p-nilpotent groups and supersolvable groups.
假设对于G的每个非循环Sylow子群P有一个子群D,使得1<|D|<|P|,且P的所有阶为|D|和2|D|(若P是非交换2-群且|P:D|>2)的子群H是G的正规嵌入子群,得到G为p-幂零群以及超可解群的一些充分条件,部分结果被推广到群系。
6) non-solvable group
非可解群
1.
Let G be a finite non-solvable group and Z(G)=1.
设G是有限非可解群且Z(G)=1。
2.
In this paper, we have proved the following:Theorem Let G be a finite non-solvable group and p be the smallest odd prime divisor of the order of G.
证明了：定理设Ｇ为有限非可解群，ｐ为｜Ｇ｜的最小奇素因子。
补充资料：非想非非想处天
1.佛教语。即三界中无色界第四天。此天没有欲望与物质﹐仅有微妙的思想。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条