All Questions

Let $G$ be a connected split reductive group over $\mathbb{Z}$. Let $n$ be a positive integer. Let $i_n(q)$ be the number of elements of $G(\mathbb{F}_q)$ satisfying $x^n=1$. Question: Is there a &...

I'm looking for references for the following statements, which I believe are true: Let $G$ be a simply connected simple linear algebraic group over a finite field $k$ of cardinality $q\ge 4$. Let $Z\...

Let $K$ be a finite field, let $n\ge 1$ be an integer and let $G=\mathrm{GL}(n,K)$ be acting linearly on a finite dimensional $K$-vector space $V$. Although $G$ is a reductive group, it is not ...

I'm interested in finding all groups for which the group operation (and inverse map) may be implemented using finite field arithmetic. I've done some searching and have come across "algebraic groups",...