Characterization of modular frobenius groups of special type

In this article, we first investigate the properties of modular Frobenius groups. Then, we consider the case that G' is a minimal normal subgroup of a modular Frobenius group G. We give the complete classification of G when G' as a modular Frobenius kernel has no more than four conjugacy classes in G.     

矩阵Frobenius范数不等式

1 引言与引理 矩阵范数与矩阵奇异值问题是数值代数的重要课题,并在矩阵扰动分析,数值计算等分支中起着重要作用.国内外学者对此已作了大量研究.     

Thompson’s conjecture for Lie type groups E 7(q)

In this article, we prove a conjecture of Thompson for an infinite class of simple groups of Lie type E ₇(q). More precisely, we show that every finite group G with the properties Z(G) = 1 and cs(G) = cs(E ₇(q)) is necessarily isomorphic to E ₇(q), where cs(G) and Z(G) are the set of lengths of conjugacy classes of G and the center of G respectively.     

所有子群皆交换或正规的有限群

本文研究所有子群皆交换或正规的有限群. 我们获得了非幂零的情形的一个特征刻画, 也给出了幂零情形的一些性质.     

关于格序群的极大素子群

研究了格序群的极大素子群的性质以及由素子群根系确定的几种格序群类的结构。     

有限群的PCM-子群

本文研究了有限群的超可解性.利用Fitting子群的某些特殊子群的PCM性质对有限群结构的影响,获得了超可解群的一些充要条件.     

关于有限群的p-超可解性

本文研究了有限群的p-超可解性,利用子群的s-条件置换性及Sylow子群的极大子群对有限群结构的影响,得到了一个群为p-超可解群的一些充分必要条件.     

特征标表中零点个数很少的有限可解群

（１）与（２）均曾研究过有某特征标恰在两个共轭类上取非零值的有限群。本文讨论上述情形的另一极端,即每个不可约特征标至多在ｐ个共轭类上取零值的有限可解群,这里ｐ为群阶的最小素因子,通过对极小非交换商群的分析,我们将刻划这类群的结构。     

A CHARACTERIZATION OF LOCALLY COMPACT INNER AMENABLE GROUPS

For locally compact groups G, Kuan Yuan studied a notion of inner amenability groups, that is, if there exists an inner invariant mean on G. In this article, among other things, the author investigates the inner amenability on a locally compact group G. The author gives sufficient conditions and some necessary conditions about G to have an inner invariant mean.     

子群交换度对群结构的影响

本文研究了子群交换度与有限群结构的关系.利用子群交换度的数量性质,获得了循环群和2n阶的广义四元数群的一个新刻画.     

SOME SUBGROUPS OF THE EXTENDED HECKE GROUPS (H)(λq)

The authors consider the extended Hecke groups H(λq) generated by T(z) =-1 / z, S(z) = -1/(z+λq) and R(z) = 1 / -z with λq = 2cos(π/q) for q ≥ 3 an integer. Inthis paper, the even subgroup He(λq), the second commutator subgroup H"(λq) and theprincipal congruence subgroups Hp(λq) of the extended Hecke groups H(λq) are studied.Also, relations between them are given.     

二次极大子群中2阶及4阶循环子群拟中心的有限群

本文讨论2阶及4阶循环子群对群结构的影响．证明二次极大子群中2阶及4阶循环子群拟中心的有限群G同构于下列群之一：(1)G为2-闭群；(2)G为2-幂零群；(3)G≌S，；(4)G=PQ．其中P为2^4阶广义四元数群，Q≌C3；(5)G≌A5或SL(2，5)．     

ON ABELIAN AUTOMORPHISM GROUPS OF SURFACES OF GENERAL TYPE

1.IntroductionItiswell-knownthatforacomplexcurveofgenusg22,itstotalautomorphismgroup(resp.abelianautomorphismgroup)isoforderS84(g-l)=42degKC(resp.S4g 4),whereKCisthecanonicaldivisorofC(cL[3,4]).Itisanintriguingproblemtogeneralisetheseboundstohigherdimensions.Severalauthorshavestudiedthisproblem(see[5,6]fordetails).Recently,Xiaohasgeneralisedtheseresultstosurfacesofgeneraltype,ingoodanalogywiththecaseofcurves.HehasprovedthatforacomplexminimalsmoothprojectivesurfaceSofgeneraltype,itstota1au…     

ON THE SUBGROUP LATTICE CHARACTERIZATION OF FINITE SIMPLE GROUPS OF LIE TYPE

Any finite simple group of Lie type is proved to be determined by its subgroup lattice up to isomorphism.     

二元域上线性群的纯数量刻画

本文给出了仅用元的阶之集对二元域上小阶线性群及其自同构群的刻画.指出并纠正了文[5]中的错误.     

具有给定Sylow-子群正规化子的有限群

本文研究了部分Sylow-子群的正规化子属于某群系且具有给定指数的有限{ p,q}-可解群,利用Sylow-子群正规化子的性质,获得了相关群的一个分类定理,并给出了若干推论.     

一类2nm(m为奇数)阶有限群的构造

本文研究了一类2nm(m为奇数)阶有限群的构造,利用解数论同余方程的方法和群的扩张理论等知识,得到了具有奇数m阶循环正规子群、其补子群为循环群的2nm阶有限群的构造及相关的计数定理.