1) cyclic maximal subgroup
循环极大子群
1.
This article makes use of the results of p-group theory, giving the number of subgroups with order pk of p-group with cyclic maximal subgroup.
利用p-群的理论,给出了具有循环极大子群的p-群的各阶子群的个数,在此基础上确定了各阶非平凡子群的个数均为p+1的p-群的完全分类。
2.
Supposing G is a p-group with cyclic maximal subgroup,p is an prime number.
设G是具有循环极大子群的p~n阶群,p为素数。
2) maximal torus subgroup
极大环面子群
3) cyclic subgroup
循环子群
1.
With respect to conjugacy,the cyclic subgroups of order 6 contained in GL(4,Z) are discussed.
从共轭的角度讨论了GL(4,Z)的 6阶循环子
2.
In this paper,the author describes the results of the number of subgroups in a group of order n,raises the guess that the lower bound of the number of subgroup is T(n),discusses the number of cyclic subgroup and the number of maximal subgroup in a commutative group of order n,studies structure of some groups.
综述了n阶群的子群个数的一些结果,提出子群个数的下界是T(n)的猜想,讨论n阶交换群的循环子群的个数与极大子群的个数,研究了一些群的构造。
3.
We denote by n(G) the number of subgroups of minimum coverings by subgroups of G,and denote by n_c(G) the number of subgroups of minimum coverings by cyclic subgroups of G,and denote by n_a(G) the number of subgroups of minimum coverings by Abelian subgroups of G,then(1)3≤n(G)≤|G|-1,(2)n_c(C_p×…×C_p)m个=pm-1+…+p+1,where m≥2,(3)n_c(C_pr×C_p)=r(p-1)+2,where r≥1,(4)n_a(C_pr×C_ps)=p+1,where r≥s≥1.
设p为素数,G是非循环有限群,群G的最小子群覆盖所包含的子群个数记为n(G),群G的最小循环子群覆盖所包含的子群个数记为nc(G),群G的最小Abel子群覆盖所包含的子群个数记为na(G),则3≤n(G)≤|G|-1,nc(Cp×…×Cp)m个=pm-1+…+p+1(m≥2),nc(Cpr×Cp)=r(p-1)+2(r≥1),na(Cpr×Cps)=p+1(r≥s≥1)。
4) maximal subgroup
极大子群
1.
A type of maximal subgroups of special orthogonal groups over local rings;
局部环上特殊正交群的一类极大子群
2.
Classification of finite groups whose maximal subgroups are Dedekind groups.;
极大子群均为Dedekind群的群
3.
Characterization of Sporadic Simple Groups with the Orders of Groups and the Sets of Indexes of Maximal Subgroups;
用阶和极大子群指数之集刻划散在单群
5) maximal subgroups
极大子群
1.
On the Intersection of Two Special Maximal Subgroups;
两类特殊的极大子群的交
2.
On the s-θ-completions of maximal subgroups and the π-solvability of a finite group
有限群极大子群的s-θ-完备与π-可解性
3.
Studied the solvabilty of finite group by the theta pairs of only one special maximal subgroups,obtained a series of new results about the solvability of finite group.
主要研究有限群的某一类特殊的极大子群,并且考察这类极大子群的θ-子群偶对该有限群结构的影响,从而得出有限群可解的几个充分条件。
补充资料：极大紧子群
极大紧子群
maximal compact subgroup
极大紧子群[叮.油般】c伽声Ct，纯r叨p;M毗，M幼I，H明KOMn毗“a，n叭印ynna」，拓扑群G的 一个紧子群(见紧群(comPact grouP))K CG，它不作为真子群被包含在G的任何紧子群内.例如，尤二50(n)对于G=SL(n，R)，K二{e}对于一个可解单连通Lie群G. 在任意群G里，极大紧子群不一定存在(例如，G“CL(V)，V是一个无限维Hilbert空间)，而一且即使存在，它们之间也可能有不同构的. Lie群的极大紧子群已被广泛地研究.如果G是一个连通Lie群，那么G的任意紧子群都被包含在某个极大紧子群内(特别，极大紧子群一定存在)，并且G的一切极大紧子群都是连通的且彼此共扼.群G的空间微分同胚于KxR”.因此，很多关于Lie群的拓扑问题都归结为紧玩群(Lie gro叩，com-pact)相应的问题.
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