Weakly commensurableS-arithmetic subgroups in almost simple algebraic groups of types B and C

Algebraic Groups, Lie Groups, and their Arithmetic Subgroups

This work is a modern exposition of the theory of algebraic group schemes, Lie groups, and their arithmetic subgroups. It supersedes Algebraic Groups and Arithmetic Groups. This file only contains the front matter. For the rest, see Single paper copies for noncommercial personal use may be made without explicit permission from the copyright holder. Preface For one who attempts to unravel the st...

Algebraic Groups and Arithmetic Groups

Some good-filtration subgroups of simple algebraic groups

Let G be a connected and reductive algebraic group over an algebraically closed field of characteristic p > 0. An interesting class of representations of G consists of those G-modules having a good filtration – i.e. a filtration whose layers are the induced highest weight modules obtained as the space of global sections of G-linearized line bundles on the flag variety of G. Let H ⊂ G be a conne...

On weakly $mathfrak{F}_{s}$-quasinormal subgroups of finite groups

Let $mathfrak{F}$ be a formation and $G$ a finite group. A subgroup $H$ of $G$ is said to be weakly $mathfrak{F}_{s}$-quasinormal in $G$ if $G$ has an $S$-quasinormal subgroup $T$ such that $HT$ is $S$-quasinormal in $G$ and $(Hcap T)H_{G}/H_{G}leq Z_{mathfrak{F}}(G/H_{G})$, where $Z_{mathfrak{F}}(G/H_{G})$ denotes the $mathfrak{F}$-hypercenter of $G/H_{G}$. In this paper, we study the structur...

On the Exponential Map of Almost Simple Real Algebraic Groups

One of the basic problems for Lie groups is to describe the image of the exponential map. A Lie group H is called exponential resp. weakly exponential if its exponential map is surjective resp. has dense image in H . In this paper we classify all exponential groups which are identity components of almost simple real algebraic groups. The weakly exponential groups of this type were determined in...