Bounded Rank Subgroups of Coxeter Groups, Artin Groups and One-Relator Groups with Torsion

We obtain a number of results regarding the freeness of subgroupsof Coxeter groups, Artin groups and one-relator groups withtorsion. In the case of Coxeter groups, we also obtain resultson quasiconvexity and subgroup separability. 2000 MathematicsSubject Classification 20F65, 20F55, 20F36, 20F06.     

作用在有限线性空间上基柱为2F4(q)的几乎单群

本文研究了基柱同构于2F4(q)的线传递的几乎单群.利用了有限线性空间上线传递的自同构群的经典结论,以及2F4(q)的阶和极大子群等性质,获得了点稳定子群和线稳定子群的分类.     

Shmel’kin embeddings for abstract and profinite groups

The Magnus embedding is well known: given a group A=F/R, where F is a free group, the group F/[R, R] can be represented as a subgroup of a semidirect product AT, where T is an additive group of a free Z A-module. Shmel’kin genralized this construction and found an embedding for F/V(R), where V(R) is the verbal subgroup of R corresponding to a variety V. Later, he treated F as a free product of arbitrary groups, and on condition that R is contained in a Cartesian subgroup of the product, pointed out an embedding for F/V(R). Here, we combine both these Shmel’kin embeddings and weaken the condition on R, by assuming that F is a free product of groups A_i (iεI) and a free group X, and that its normal subgroup R has trivial intersection with each factor A_i. Subject to these conditions, an embedding for F/V(R) is found; we cell it the generalized Shmel’kin embedding. For the case where V is an Abelian variety of groups, a criterion is specified determining whether elements of AT belong to an embedded group F/V(R). Similar results are proved also for profinite groups. Supported by RFFR grant No. 99-01-00567. Translated fromAlgebra i Logika, Vol. 38, No. 5, pp. 598–612, September–October, 1999.     

A Generalization of <Emphasis Type="Italic">T</Emphasis>-Groups

This paper identifies a certain class of locally supersoluble groups (called soluble hall-T groups) which contains the soluble T-groups as well as the nilpotent groups. The main result states that the product of a normal soluble hall-T subgroup and a subnormal locally supersoluble subgroup is always locally supersoluble.AMS Subject Classification (1991): 20E25, 20F16, 20F19     

On a Class of Supersoluble Groups

This paper identifies a class of supersoluble groups, called finitely generated hallsoging groups. The main result states that the product of a normal finitely generated hall-soging subgroup and a subnormal supersoluble subgroup is always supersoluble.AMS Subject Classification (1991): 20F16, 20F19, 20E25.     

关于$\mathcal{F}$-S-可补子群

设$\mathcal{F}$是一个群类. 群$G$的子群$H$称为在$G$中$\mathcal{F}$-S-可补的，如果存在$G$的一个子群$K$,使得$G=HK$且$K/K\cap{H_G}\in\mathcal{F}$, 其中$H_G=\bigcap_{g\in G}H^g$是包含在$H$中的$G$的最大正规子群．本文利用子群的$\mathcal{F}$-S-可补性, 给出了有限群的可解性, 超可解性和幂零性的一些新的刻画. 应用这些结果, 我们可以得到一系列推论, 其中包括有关已知的著名结果.     

The conjugacy and isomorphism problems for combable groups

There exist combable groups in which the conjugacy problem is unsolvable. The isomorphism problem is unsolvable for certain recursive sequences of finite presentations of combable groups. Mathematics Subject Classification(2000): 20F67, 20F10, 20F65This research was supported by an EPSRC Advanced Fellowship     

A conjecture of Abe-Iiyori and the Ree groups 2F4(q),Ⅱ

In this paper the author has solved a problem of Abe and liyori for the finite simple groups 2F4(q) and 2F4(2)'.     

A conjecture of Abe-Iiyori and the Ree groups ~2F_4(q),Ⅱ

In this paper the author has solved a problem of Abe and liyori for the finite simple groups 2F4(q) and 2F4(2)'.     

On Local Descent to Metaplectic Groups and Local Theta Correspondence

Let F be a p-adic field of characteristic 0.We study a twisted local descent construction for the metaplectic groups Sp_(2 n)(F),and also its relation to the corresponding local descent construction for odd special orthogonal groups via local theta correspondence.In consequence,we show that this descent construction gives irreducible supercuspidal genuine representations of Sp_(2n)(-F) parametrized by a simple local L-parameter φ_τ corresponding to an irreducible supercuspidal representation τ of GL_(2n)(F) of symplectic type,and the genericity of the representations constructed can be indicated by a local epsilon factor condition.In particular,this local descent construction recovers the local Shimura correspondence for supercuspidal representations.