The order of elements in Sylow p-subgroups of the symmetric group

Define a random variable ξ_n by choosing a conjugacy class C of the Sylow p-subgroup of S_pn by random, and let ξ_n be the logarithm of the order of an element in C. We show that ξ_n has bounded variance and mean order log n /log p +O(1), which differs greatly from the average order of elements chosen with equal probability. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Criterion for Non-Simplicity of Groups with Involutions

We settle Question 10.61, posed by A. Sozutov in the Kourovka Notebook, for the case where .     

Quasi-isometric rigidity of nonuniform lattices in higher rank symmetric spaces

We compute the quasi-isometry group of an irreducible nonuniform lattice in a semisimple Lie group with finite center and no rank one factors, and show that any two such lattices are quasi-isometric if and only if they are commensurable up to conjugation.

     

半次覆盖远离子群和有限群的可解性

本文定义了有限群的半次覆盖远离子群概念,研究了半次覆盖远离子群和有限群的可解性问题.利用某些半次覆盖远离子群刻划了有限群的可解性,得到了若所有的sylow子群(或极大子群)半次覆盖远离则群可解,推广了文献[6]中的结果.     

The Mapping Class Group of a Nonorientable Surface is Generated by Three Elements and by Four Involutions

We prove that the mapping class group of a closed nonorientable surface is generated by three elements and by four involutions Mathematics Subject Classification (2000). primary: 57N05; secondary: 20F38, 20F05.     

The Uniqueness of the Actions of Certain Branch Groups on Rooted Trees

It is proved that in many cases of interest the actions of groups on rooted trees can be recovered from the structure of the groups. The results apply to most of the groups introduced by the first author and to the Gupta–Sidki groups; they are proved in the wider context of branch groups satisfying two natural conditions.     

9中心化子群的结构

记#Cent（G）为群G的所有互不相同的元素的中心化子个数．如果#Cent（G）=礼,则称G为n中心化子群．本文给出了9中心化子群的结构．     

弱次正规子群和有限群的可解性

如果群G有次正规子群K使HK⊿⊿G且H∩K⊿⊿G,那么子群H被称做群G的弱次正规子群.利用极大子群Sylow子群或Sylow子群正规化子的子群的弱次正规性得到了一些关于有限群的可解性结论.     

有限群的$Phi$-$tau$-可补子群

假设$tau$是一个子群算子, $H$是有限群$G$的一个$p$-子群. 令 $bar{G}=G/H_{G}$且$bar{H}=H/H_{G}$, 如果$bar{G}$有一个次正规子群$bar{T}$ 和一个包含于$bar{H}$ 的$tau$-子群$bar{S}$满足$bar{G}=bar{H}bar{T}$且$bar{H}capbar{T}leq bar{S}Phi(bar{H})$, 就称$H$是$G$的一个$Phi$-$tau$- 可补子群. 文章通过讨论群$G$的准素数子群的$Phi$-$tau$-可补性给出了超循环嵌入和$p$-幂零性的一些新的特征.     

Solitary Solvable Groups

A subgroup H of a group G is a solitary subgroup of G if G does not contain another isomorphic copy of H. Combining together the concepts of solitary subgroups and solvable groups, we define (normal) solitary solvable groups and (normal) strongly solitary solvable groups. We derive several results that hold for these groups and we discuss classes of groups that, under certain hypotheses, are (normal) solitary solvable and (normal) strongly solitary solvable. We also derive several results about p-groups that are solitary solvable.