Suzuki-Ree群的特征性质

本文证明了如下定理定理.设G是群,M为Suzuki-Ree群,则G≌M当且仅当:(1)π_e(G)=π_e(M),其中π_e(G)记为G中元的阶之集;(2)|G|=|M|.     

关于有限群不可约特征标零点的一点注记

在这篇文章中,我们分类了每一个非线性不可约特征标的零点集最多由$3$个共轭类组成的有限亚交换群的结构.     

J_1与PSL_2(2~n)的特征性质

用“阶”的概念刻划有限单群由来已久.近年来,又有不少作者做了这方面的工作.但这些刻划都用了群的单性和其他一些概念.在这篇短文中,我们继续以前的讨论,只用“群的阶”和“元的阶”这两个最简单的概念对小Janko单群J_1进行刻划,得出J_1的特征性质是(本文所讨论的群恒为有限):     

关于图的基本群的正规子群的指数

本文主要研究图的基本群的正规子群的指数何时成为任意正整数的条件．主要讨论的群类有:有限生成的无扭幂零群、自由群、多重无限循环群等．     

中心外的同阶元必共轭的有限群

证明了在有限群G中, 若中心外的任何两个同阶的元素均共轭, 则G为交换群或者G≌S₃.     

Finite Groups in Which the Orders of Elements Are Continuous Integers

R.Brandl has put the following question:Whether for any positive integer nthere exists a finite group such that the orders of all elements are ≤n and foreach m≤n there exists an element of order m.We call such finite groups OC_ngroups.B.H.Neumann has studied such general groups with n≤3.For all n≤7such finite groups、exist.For example,the alternating group A_7 is an OC_7 group. In this paper we mainly prove the following two theorems.     

以方程(组)为中心展开高等代数课程的教学

以方程(组)为中心阐述了高等代数各部分内容的内在联系,给出了高等代数课程教学的一种新的教学模式.     

Finite Groups Whose Element Orders Are Consecutive Integers

There are various characterizations of groups by conditions on the orders of itselements.For example,in[2]and[1]the finite group all of whose elements haveprime power order have been classified.In[4—7]some simple groups have beencharacterized by conditions on the orders of its elements and B.H.Neumann[3]has determined all groups whose elements have orders 1,2 and 3.The latter groupsare OC_3 groups in the sense of the following     

Mathieu群的一个特征性质

R.G.Stanton等曾先后以群阶和单性为条件刻划了五个Mathieu群M_i,i=11,12,22,23,24。本文仅用群G的元的阶之集π_e(G)为条件来刻划这些群,得到如下结论。 设G是有限群,若π_e(G)=π_e(M_i),则GM_i,i=11,22,23,24。又若π_e(G)=π_e(M_12),且2~14×|G|,则GM_12。