自由部分交换群的抛物与拟抛物子群

Perfect models for finite Coxeter groups

A model for a finite group is a set of linear characters of subgroups that can be induced to obtain every irreducible character exactly once. A perfect model for a finite Coxeter group is a model in which the relevant subgroups are the quasiparabolic centralizers of perfect involutions. In prior work, we showed that perfect models give rise to interesting examples of $W$-graphs. Here, we classify which finite Coxeter groups have perfect models. Specifically, we prove that the irreducible finite Coxeter groups with perfect models are those of types $\mathsf{A}_{n}$, $\mathsf{B}_n$, $\mathsf{D}_…

关于某些分形群的抛物子群和Hecke代数

On Parabolic Subgroups and Hecke Algebras of Some Fractal Groups

研究了分支型分形群的子群结构、Hecke代数、拟正则表示和渐近性质。引入抛物子群，证明了它们是弱极大的，并且相应的拟正则表示是不可约的。这些（无限维）表示近似的有限维准正则表示。与这些抛物子群相关联的Hecke代数是交换的，所以有限拟正则表示的不可约分支的分解由抛物子群的双陪集给出.由于我们的结果是从有限指数子群的考虑出发的，所以它们也适用于群G的profinite完备化$\hat G$。在数学GR/9910102中，所涉及的表示具有有趣的光谱特性。本文作为一个群论对应的研究中mentionned文件。我们更仔细地研究了分形群的几个例子，并在这样做展示了一个挠自由分支的第一个例子只是-无限群。我们还给出了一个新的例子，即分支恰好-中间增长的无限群，并给出了它的生成元和关系子的L-型表示。

One-relator quotients of Partially Commutative Groups

We generalise a key result of one-relator group theory, namely Magnus's Freiheitssatz, to partially commutative groups, under sufficiently strong conditions on the relator. The main theorem shows that under our conditions, on an element $r$ of a partially commutative group $\mathbb{G}$, certain Magnus subgroups embed in the quotient $G=\mathbb{G}/N(r)$; that if $r=s^n$ has root $s$ in $\mathbb{G}$ then the order of $s$ in $G$ is $n$, and under slightly stronger conditions that the word problem of $G$ is decidable. We also give conditions under which the question of which Magnus subgroups of $\…

幂等分解与Chevalley群的正规结构的新认识

A new look at the decomposition of unipotents and the normal structure of Chevalley groups

目前的文章继续一系列的文件分解的unipotents及其应用。设$G(Φ,R)$是交换环$R$上具有约化不可约根系$Φ$的Chevalley群.修复$h\in G(Φ,R)$。称一个元素$a\in G(Φ,R)$为“好”，如果它位于一个抛物子群的幂幺根中，而$h$与$a$的共轭属于另一个真抛物子群（这里我们假设所有抛物都包含一个给定的分裂极大环面）。幂幺元的分解是将根幂幺元表示为“好”元素的乘积。这种分解的存在性意味着一个简单的证明的正规性的基本子群和描述的正规结构的$G(Φ,R)$。然而，分解并不适用于所有的根系。在目前的文章中，我们证明了标准的正常结构，它足以只构造一个“好”元素的通用元素的计划$G(Φ,_-)$，并构造这样一个“好”的元素。关于“好”元素是否生成整个初等群的问题将在另一篇论文中讨论（该论文的第一版是俄文）。

On the congruence kernel of isotropic groups over rings

Let R be a connected noetherian commutative ring, and let G be a simply connected reductive group over R of isotropic rank ge 2. The elementary subgroup E(R) of G(R) is the subgroup generated by the R-points U_P^+(R) and U_P^-(R) of the unipotent radicals of two opposite parabolic subgroups P^+ and P^- of G. Assume that 2 is invertible in R if G is of type B_n,C_n,F_4,G_2 and 3 is invertible in R if G is of type G_2. We prove that the congruence kernel of E(R), defined as the kernel of the natural homomorphism between the profinite completion of E(R) and the congruence completion of E(R) with …