Conway单群CO2的一个刻划

用有限群G的元的阶之集π_c(G)我们已经刻划了如下散在单群:J_1,M_(11),M_(22),M_(23),M_(24)和HS(见[1,2,3]).这篇注记继续上述工作,仅用真π_c(G)给出Conway单群CO_2的一个特征性质.本文所讨论的群均为有限,所用的符号是标准的([4]).此外,还记π(G)为群G的阶的质因子集,|π(G)|为|G|的相异质因子数.我们证明了如下结论:     

用阶刻划单群及有关课题

“群的阶”与“元的阶”是群论的两个最基本的概念,但它们在群的研究中起着重要的作用。 1902年W.Burnside提出如下著名的问题:若群G为有限生成,G中元的阶均为有限,G的阶是否有限?虽然Burnside的问题已由Golod给出了否定的答案,但它突出了“元的阶”在群的结构中的作用。     

关于某些多边形积的剩余有限性

讨论嵌入子群是循环群的有限p-群的多边形积,得到了多边形积为剩余有限的一个充分条件.     

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.     

闭2-极大子群指数为素数幂的有限群

设G为有限群, 如果G的每个非2-闭极大子群的指数均为素数幂, 那么 G-S(G)≌PSL2(7)或1, 其中S(G)为G的最大可解正规子群.     

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.     

用$\tau_e(L_2(16))$刻画$L_2(16)$

Let G be a group and πe(G) the set of element orders of G.Let k∈πe(G) and m k be the number of elements of order k in G.Letτe(G)={mk|k∈πe(G)}.In this paper,we prove that L2(16) is recognizable byτe (L2(16)).In other words,we prove that if G is a group such that τe(G)=τe(L2(16))={1,255,272,544,1088,1920},then G is isomorphic to L2(16).     

再论有限群中元的阶之集

再论有限群中元的阶之集@Ｎａｏｋｉ　Ｃｈｉｇｉｒａ@施武杰...     

关于 E.Artin 的一个问题

本文用有限单群分类定理解决了 E.Artin 所提出的如下问题:定出所有Sylow 子群的阶大于 g~(1/3)(g-|G|)的有限单群 G.