3
votes
1answer
62 views

The identity component of an algebraic group is always parabolic

Essentially I was wondering if the quotient of an algebraic group $G$ by its identity component $G^0$ is necessarily always parabolic. My argument: This seems right since $G^0$ is a closed ...
0
votes
0answers
108 views

How can I generate $\mathrm{SL}(n,\mathbb Z)$ by the subgroup $\mathrm{SL}(n-1,\mathbb Z)$ and another Element of $\mathrm{SL}(n,\mathbb Z)$?

Let $\{z_1,...,z_n\}$ be the canonical Basis of $\mathbb{Z}^n$, such that $z_i$ equals the vector $(0,\dotsc,0,i,0,\dotsc,0)$ with a 1 in the $i$th position. I want to show that the ...