1) subnormal subgroup
次正规子群
1.
In this paper, we investigate the influence of subnormal subgroups on the structure of finite groups and some sufficient conditions for solvability and a sufficient condition for supersolvability of finite groups are given.
考查了次正规子群对有限群结构的影响,得到有限群可解的若干充分条件和超可解的一个充分条件。
2.
A subgroup H of a group G is said to be S-normal in G if there exists a subnormal subgroup K of G such that G=HK and H∩ K≤H SG .
群G的一个子群H 在G 中是S 正规的,如果存在G的一个次正规子群K,使得G=HK且H∩K≤HSG,其中HSG是包含在H 中的G 的最大次正规子群。
3.
A finitely generated soluble group G has derived length at most 5 and Fitting length at most 4 if the defect of every subnormal subgroup of G does not exceed 2.
由此可以证明次正规子群的亏数均≤ 2的有限生成可解群的导出长度至多为 5 ,其幂零长度至多为 4 ,这推广了McCaughan -Stonehewer、Casolo等人的结
2) subnormal subgroups
次正规子群
1.
Considering the subnormal subgroups,some equivalent conditions for nilpotency of finite groups are given and a sufficient condition for nilpotency of finite groups is obtained.
研究次正规子群对有限群结构的影响,得到幂零群的若干等价条件和一个充分条件。
3) non-subnormal subgroup
非次正规子群
1.
In this paper, we have proved that all non-subnormal subgroups of a finite group G are conjugate if and only if G=〈a, b_1, b_2, …, b_β|a~(p~α)=1=b_1~q=b_2~q=…=b_β~q; [bi, bj]=1, i,j=1,2,…,β;b_i~a=b_(i+1), i=1,2,…,β-1; b_β~a=b_1~d1b_2~d2…b_β~dβ〉where f(x)=x~β-d_βx~(β-1)-…-d_2x-d1 is an irreducible polynomial over the field F_q, which divides x~p-1.
证明了有限群G有非次正规子群且彼此共轭的充要条件是G=〈a, b_1, b_2, …, b_β|a~(p~α)=1=b_1~q=b_2~q=…=b_β~q; [bi, bj]=1, i,j=1,2,…,β;b_i~a=b_(i+1), i=1,2,…,β-1; b_β~a=b_1~d1b_2~d2…b_β~dβ〉其f(x)=x~β-d_βx~(β-1)-…-d_2x-d1在F_q上不可约,且为x~p-1的因子。
2.
In this paper the authors mainly proved that:If the finite group G has two conjugate classes of non-subnormal subgroups H={H_1,H_2,"",H_m} and K={K_1,K_2,"",K_n},then G is soluble,and|G|has at most three prime factors,and G satisfing one of the following conditions: (1)G=H■Q,where H is a p-group which has cyclic maximal subgroups,and Q is the Sylowq-sub- group of G,p and q are different primes.
主要证明了:若有限群G只含两个非次正规子群共轭类H=(H_1,H_2,…,H_m)和K={K_1,K_2,…,K_n},则G可解。
3.
We denote the number of the conjugate classes of non-subnormal subgroups of G byμ, and have the following results: Theorem 2.
本文主要证明了所有非次正规子群形成一个共轭类的群的一些性质。
4) Fuzzy Subnormal Subgrou
Fuzzy次正规子群
1.
The Fuzzy Quasinormal Subgroups and Fuzzy Subnormal Subgroups of Finite Groups;
有限群的Fuzzy拟正规子群和Fuzzy次正规子群
5) normal subgroup
正规子群
1.
Character of group which only have n nontrivial normal subgroups
仅含n个非平凡正规子群的群的特征
2.
By using algebra of fixed point class to determine the component factors and properties of normal subgroup H of the fundamental group of the covering space, the paper studies the relation of fixed point class with fixed point class H.
本文利用不动点类的代数化 ,决定复迭空间的基本群的正规子群H的构成因素及其性质 ,研究不动点类与H不动点类的关系。
3.
Based on the Rough theory, a rough subgroup with respect to a normal subgroup of a group is discussed, and some properties of the lower and the upper approximations in a group are studied.
基于粗糙集理论 ,对一个群的子集关于正规子群的粗糙近似子群作了探讨 ,并研究了一个群的上、下近似的性
6) normal subgroups
正规子群
1.
Su Xiang Ying and Wang Pin Chao obtained some sufficient conditions of supersoluble groups by studying semi normal subgroups of finite groups[1,2,7].
文献 [1 ]引入的半正规子群 ,对有限群结构有重要的影响 [1 ,2 ,7] 。
2.
Considering the subnormal subgroups,some equivalent conditions for nilpotency of finite groups are given and a sufficient condition for nilpotency of finite groups is obtained.
研究次正规子群对有限群结构的影响,得到幂零群的若干等价条件和一个充分条件。
补充资料：正规子群
正规子群
normal srihgroqi
正规子群f.川口日，鲍”，;”o州a刀研‘‘举月“犯月‘]，正规除子(加m司divisor)，不变子群(访珑币田吐sub-罗〕uP)群G的子群H，使得G模H的左分解与右分解相同.换言之，对于任意元素a6G，陪集aH和Ha(作为集合)相等.这时亦称H在G中正规，记作H且G:如果还有H笋G，则记作H阅G.子群H在G中正规当且仅当它包含其任意元素的所有G共辘(见共辘元(conju即把日翻笠nis))，即H“住H.正规子群还可以定义为与其所有的共扼都相等的子群，因而也被称为自共扼子群(货扩·。功火势忱subgro叩). 对于任意同态(hOIno加甲恤m)州G~G’，G中被映成G’的单位元的全体元素组成的集合K(即同态毋的核(kenle!of血加伽曲印比m))是G的一个正规子群.反之，G的任一正规子群都是某个同态的核.特别地，K是映到商群(q叩血ntgro叩)G/K的自然同态的核. 对于任意正规子群的集合，它们的交仍是正规的，由G的任意一族正规子群生成的子群仍在G中正规.0.A.物a，叱a撰【补注】群G的子群H是正规的，如果对所有的g‘G有g一’Hg=H，或者等价地，其正规化子N。(H)=G，见子集的正规化子(non工以止况r of a suh记t).正规子群亦称为不变子群(运论由以su地”叩)，因为它在G的内自同构〔~auto伽rp比m)x巨尸=g一，xg(g‘G)下是不变的.在全体自同构下不变的子群称为全不变子群(蒯y一访招山ntsu地加uP)，或者特征子群(d朋沈施加su琢ouP).在全体自同态下不变的子群称为全特征子群(刘y‘玩‘‘泊由tic su地阳叩).【译注】有的书将全体自同态下不变的子群称为〔完)全不变子群，而在全体自同构下不变的子群称为特征子群，如见[AI]，[BI].
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