一类pq2阶群的自同构群

得到了如下定理:设p,q是奇素数,且q相似文献   

特殊射影线性群L_5(q)的OD-刻画

若存在k个互不同构的群与群G具有相同的群阶和素图度数序列,则称群G是可k重OD-刻画的.特别地,若k=1,则称群G是OD-刻画群.利用群阶和素图度数序列证明了特殊射影线性群L5(q)是OD-刻画群,其中q(2≤q15)是素数的方幂.     

用非交换图刻画L3(q)

令G是一个有限群,其非交换图▽（G）如下定义：顶点集合▽（G）是G／Z（G）,当两条边x与y的换位子不等于单位元时x与y相连.我们证明了如果G是一个有限群,且▽（G）≌▽（M）,其中M=L3（q）,q=pn,p是素数n∈N,则G≌M.     

关于超可解群的若干结果

利用弱拟正规子群,得到有限群成为超可解群的一系列充分条件．     

关于 Sylow 定理的应用

通过例题的形式给出了《抽象代数》的经典内容——Sylow定理的一些典型应用,加深了对Sylow定理的理解,凸显了它的重要性.     

关于Thompson猜想与AAM猜想

本文研究了有限(几乎)单群的非交换图刻画问题.利用有限几乎单群的阶分量理论,证明了对于具有非连通素图的有限单群,AAM猜想成立,同时也证明了某砦几乎单群也能被其非交换图刻画.上述结果推广了文献f131的结果.

Abstract：

In this article,we discuss the characterization of some finite(almost)simple groups by their non-commuting graphs.By using the theory of order components of finite almost simple groups,we prove that AAM's conjecture is true for all finite simple groups with non-connected prime graphs.Moreover,we prove that some almost simple groups can be also characterized by their non-commuting graphs.All the above results generalize those results in[13].     

单群L_3(9)的OD-刻画(英文)

利用有限群的群阶和度数型对射影特殊线性单群L3(9)进行了刻画,得到了如下定理:设G是一有限群,若D(G)=D(L3(9))且|G|=|L3(9)|,则G≌L3(9).     

交错群A16的OD-刻画

利用有限群的群阶和它的度数型对具有连通素图的交错群A16进行了刻画,得到了如下定理：设G是一有限群,若D（G）=D（A）且｜G｜=｜A｜,则G=A16。     

OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U6（2）

Let G be a finite group and π(G) = { p 1 , p 2 , ··· , p k } be the set of the primes dividing the order of G. We define its prime graph Γ(G) as follows. The vertex set of this graph is π(G), and two distinct vertices p, q are joined by an edge if and only if pq ∈π e (G). In this case, we write p ～ q. For p ∈π(G), put deg(p) := |{ q ∈π(G) | p ～ q }| , which is called the degree of p. We also define D(G) := (deg(p 1 ), deg(p 2 ), ··· , deg(p k )), where p 1 < p 2 < ··· < p k , which is called the degree pattern of G. We say a group G is k-fold OD-characterizable if there exist exactly k non-isomorphic finite groups with the same order and degree pattern as G. Specially, a 1-fold OD-characterizable group is simply called an OD-characterizable group. Let L := U 6 (2). In this article, we classify all finite groups with the same order and degree pattern as an almost simple groups related to L. In fact, we prove that L and L.2 are OD-characterizable, L.3 is 3-fold OD-characterizable, and L.S 3 is 5-fold OD-characterizable.     

L4(4)的非交换图刻画

令G是一个有限非交换群.如下定义群G的非交换图▽(G):其顶点集是G\Z(G),任意两个顶点x和y相连的充要条件是[x,y]≠1.2006年, Abdollahi A.,Akbari S.和Maimani H.R.提出了如下猜想:若群G满足条件▽(G)≌▽(M),其中M是有限非交换单群,则G≌M.尽管该猜想对于具有非连通素图的有限单群以及交错群A10足成立的,但是人们仍不知道它对于除A10外的具有连通素图的有限单群是否成立.该文证明了上述猜想对于射影特殊线性单群L4(4)也是成立的.