All Questions

If $k$ is a commutative field of characteristic $p>0$, then the map $$ \theta \colon \mathrm{GL}_p(k) \to \mathrm{SL}_p(k) \colon A = (a_{ij}) \mapsto (\det A)^{-1} (a_{ij}^p) $$ is a group ...

Let $G$ be a discrete group and let $V$ be a vector space over a field of characteristic $0$ upon which $G$ acts linearly. I'm looking for the right terminology for the following situation: for all $...

I've encountered in Bass, Lubotzky, Magid, and Mozes - The proalgebraic completion of rigid groups (Remark 1. p. 7) the following terminology: A normal subgroup $N$ of $G$ is observable if every $N$-...

Over the years, I have heard two different proposed answers to this question. It has something to do with parabolic elements of $SL(2,\mathbb{R})$. This sounds plausible, but I haven't heard a really ...

Suppose $\rho : G \to PGL_n(k)$ is a projective representation of a group $G$ over a field $k$. It's classical that the obstruction to lifting this to a linear representation $G \to GL_n(k)$ is a ...