1) 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) 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。
5) covering by cyclic Subgroup
循环子群覆盖
6) cycle group
循环群
1.
This paper proposes a new group signature scheme derived from a proxy signature scheme which can solve the above problems,and the order of cycle group adopted by this scheme is a public parameter,and the length of group public key is fixed.
本文提出一种从代理签名演化而来的新的群签名方案,能够解决这一问题,并且本方案所采用的循环群的阶为一公开参数,群公钥长度固定。
2.
The idea making use of producing matrix on the cycle group,this paper has discussed the property about R-grade cycle matrix and the question about R-grade cycle matrix diagonalization,brought to light the relations between one type diagonalization similar matrix and R-grade cycle matrix.
本文利用循环群上生成矩阵的方法,讨论n阶R循环矩阵的性质与对角化的问题,揭示一类可对角化相似矩阵与R循环矩阵的关系。
3.
It is prove that groups of order p2 can be divided into two kinds in the isomorphism sense:(1) cycle group;(2)commutative group which can be written as a product of two cycle proper-subgroup of order p.
证明了在同构意义下p2阶群共有两类:一类是循环群,一类是可分解为两个p阶真循环子群乘积的可换群。
补充资料：多循环群
多循环群
polycydic group
和指数增长(pdyno而al and expollellhal脚wthingro叩5 alldalgebn巧).而若它是多项式增长的，则它是多循环的并且是殆幂零的(司most ni】Potent)(即它包含一指数有限的幂零子群)“A2}，走A3)).若M是完全的、连通的、局部齐性的Ri洲znn湘衫，则它的同伦群兀、(M)的每个可解子群是多循环群. 提出每个多循环群都同构于整数上的一个矩阵群的定理是在【A51中首先证明的.提出多循环群就是满足关于子群的极大条件(the nlaxilllulnconditionfor subgrou声)的可解群的定理见【A7〕.多循环群l州y仔比c gr阅p;noJUI从栩“，ec肥印，。a] 一个具有多循环列(polw界】ics~)的群，即具有因子群均为循环群的次正规列的群(见子群列(sub-gro叩se眼)).多循环群类与满足子群的极大条件的可解群类一致，它对子群、商群和群扩张封闭.在任一多循环群列中无限因子群的个数是多循环群的一个不变量(多循环维数(训1界犷】ic din℃nsion)).多循环群的全形(见群的全形(hofomo印h of a grouP”同构于整数环上的一个矩阵群，这使我们可以把来自代数几何、数论和p进分析中的方法用到多循环群的理论中去.设k为有限域的一代数扩域而G为多循环群的一有限扩张，那么任一单kG模在k上是有限维的.在任意群中，两个局部多循环的正规子群的积还是局部多循环子群.【补注】整数环上的每个可解线性群都是多循环群(IAI」).可解群是多循环群，当且仅当它的每个子群都是有限生成的“A2”·M俪卜认七甘宇浮(Mil-nor一WOlf Uloorem)提出，有限生成可解群或者是多项式增长或者是指数增长的(见群和代数中的多项式增长
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