关于剩余有限群的Profinite完备化

设G是个剩余有限群,本文深入地讨论了G的Profinite完备化之间的关系,得到了整齐的结果.     

Profinite群的共轭分离性和全形

本文讨论了profinite群的共轭分离性和全形，把关于无限群的结果推广到了profinite群。     

有限π-可分群的逆向极限

本文给出了P.Hall等人关于有限π-可分群和有限可解群的部分工作的Profinite形式     

有限π-可分群的逆向极限

本文绘出了P.Hall等人关于有限π-可分群和有限可解群的部分工作的Profinite形式     

|A(G)|=26p2(p为奇素数)的有限Abel群G

本文根据有限Abel群G的自同构群A(G)的阶研究了群G的构造.利用有限交换群的一些性质,经过详细的理论推导,获得了|A(G)|=26p2(p为奇素数)的有限Abel群G的全部类型.     

特征与可解性

本文研究了具有不可约特征x使得x(1)²=|G:Z(G)|成立的群G的可解性,并证明了:对于这样的群G,当|Irr(G)|≤4时,G是可解群;当4<|Irr(G)|≤6时,在某些条件下,G是有解群.     

关于广义Dedekind群

如果群G的任意循环子群H满足|HG:H|≤p,其中p是素数,那么称G是C*(p)-群.若群G是有限C*(p)-p-群,则当p＞3时,该群的幂零类至多为2;若p=3,该群的幂零类至多为3,而且当cl(G)=3时,exp(G)=9;同时,若G与任意有限C*(p)-p群G × K直积是C*(p)-P-群G×K,则G是初等阿贝尔p-群.最后还对局部幂零的C*(p)-群进行了探讨.     

恰有两个子群共轭类长的有限群

设G是有限群,Ns(G)表示G的子群共轭类长构成的集合.本文研究Ns(G)中只有两个元素时有限群G的结构,在非幂零情形时给出了G的完全分类,在幂零情形时获得了G的一些性质.     

某些有限群的自同构群

令G是一个奇阶群。本文证明了:当G具有小阶时,G不能作为一个有限群的全自同构群。     

对称群的一个特征性质

设G为有限群,∑_n为n次对称群,本文证明了:G≌∑_n当且仅当|G|=|∑_n|且Π_e(G)=Π_e(∑_n),此处Π_e(G)为G中元的阶的集合。     

Grothendieck''s problem on profinite completions and representations of groups

The paper is concerned with Grothendieck's problem on profinite completions of groups. The relationship of this problem to the representation theory of finitely generated groups and to the problem of arithmeticity of Platonov are treated.To Professor A. Grothendieck on the Occasion of his 60th Birthday     

Double Coset Formulas for Profinite Groups

We show that in certain circumstances there is a sort of double coset formula for induction followed by restriction for representations of profinite groups.     

Hall共轭嵌入子群对有限群结构的影响

设群G为有限群,日为G的子群.若对任意的g∈G,日为〈H,H~g〉的Hall子群,则称子群日为G的Hall共轭嵌入子群.利用Hall共轭嵌入子群得到有限群G分别为幂零群与超可解群的若干新的判定方法.     

On Complemented Subgroups of Finite Groups

51. IntroductionIt is quite clear that the ekistence of complements for some families of subgroups of agroup gives a lot ofinfor~ion about its structure. FOr instance, Hall[6] proved that a groupG is supersoluble with elementary abelian Sylow subgroups if and only if G is complemellted,that is, every subgroup of G is comPlemeded in G. The same anchor also proved that agroup is soluble if and only if every Sylow subgroup is complemellted (see [3;I,3.5]). Morerecelltly, Arad and Wardll] pro…     

Self-similar groups in the sense of an iterated function system and their properties

The notion of self-similarity in the sense of iterated function system (IFS) for compact topological groups is given by ?. Koçak in Definition 3. In this work, first we give the definition of strong self-similar group in the sense of IFS. Then, we investigate the main properties of these groups. We also obtain the relations between profinite groups and strong self-similar groups in the sense of IFS. Finally, we construct some examples of these groups.     

Exact borel subalgebras of quasi-hereditary algebras. II

In this article, we consider the class of flat G-modules in the category of discrete modules over a profinite group G. We will appeal to a recent result of Enochs to prove that we have flat covers in this situation.     

FINITE GROUPS WITH SOME PRIMARY SUBGROUPS F-s-SUPPLEMENTED

Let F be a class of groups. A subgroup H of a group G is called F-s-supplemented in G if there exists a subgroup K of G such that G = HK and K|K ∩ H_G belongs to F. We obtain some results about the F-s-supplemented subgroups and use them to determine the structure of some groups. In particular, some new criteria of p-nilpotency, solubility, supersolubility of a group are obtained.     

The true prosoluble completion of a group: Examples and open problems

The true prosoluble completion of a group Γ is the inverse limit of the projective system of soluble quotients of Γ. Our purpose is to describe examples and to point out some natural open problems. We discuss a question of Grothendieck for profinite completions and its analogue for true prosoluble and true pronilpotent completions. Goulnara Arzhantseva and Zoran Šunić were the authors of the Appendix.     

有限$p$-幂零群的一个判定准则

设$G$为一个有限群, $H$是$G$的一个子群. 称$H$在$G$中是$s$-半置换的若对$G$的任意Sylow $p$-子群$G_p$, $HG_p=G_pH$, 其中$(p, |H|)= 1$,这里$p$是整除$G$的阶一个素数.通过假设$G$的一些子群是$s$-半置换的, 我们给出了$p$-幂零群的一个判定准则. 我们的结果推广了著名的Burnside $p$-幂零群准则.